diff --git a/.eslintrc.js b/.eslintrc.js
index 4ece48c8fd..3b4c5f7a67 100644
--- a/.eslintrc.js
+++ b/.eslintrc.js
@@ -21,7 +21,7 @@ module.exports = {
     },
     sourceType: 'module',
   },
-  plugins: ['react', 'flowtype', 'import', 'prettier'],
+  plugins: ['babel', 'react', 'flowtype', 'import', 'prettier'],
   rules: {
     // Plugin rules:
     'import/no-duplicates': 'error',
@@ -66,7 +66,9 @@ module.exports = {
     'no-extra-bind': 'error',
     'no-extra-label': 'error',
     'no-implied-eval': 'error',
-    'no-invalid-this': 'error',
+    // We use the version from the babel plugin so that `this` in a function
+    // class property doesn't give a false positive.
+    'babel/no-invalid-this': 'error',
     'no-return-await': 'error',
     'no-self-compare': 'error',
     'no-throw-literal': 'error',
diff --git a/package.json b/package.json
index 4c093368f7..093d524763 100644
--- a/package.json
+++ b/package.json
@@ -90,6 +90,9 @@
           "polyfill": false,
           "regenerator": true
         }
+      ],
+      [
+        "transform-class-properties"
       ]
     ]
   },
@@ -99,6 +102,7 @@
     "babel-eslint": "^7.2.3",
     "babel-jest": "^20.0.3",
     "babel-loader": "^7.1.2",
+    "babel-plugin-transform-class-properties": "^6.24.1",
     "babel-plugin-transform-runtime": "^6.23.0",
     "babel-polyfill": "^6.26.0",
     "babel-preset-env": "^1.6.1",
@@ -109,6 +113,7 @@
     "devtools-license-check": "^0.5.0",
     "eslint": "^4.12.0",
     "eslint-config-prettier": "^2.4.0",
+    "eslint-plugin-babel": "^4.1.2",
     "eslint-plugin-flowtype": "^2.39.1",
     "eslint-plugin-import": "^2.8.0",
     "eslint-plugin-prettier": "^2.2.0",
diff --git a/src/components/app/FooterLinks.js b/src/components/app/FooterLinks.js
index c5ee1bb789..28845bf07d 100644
--- a/src/components/app/FooterLinks.js
+++ b/src/components/app/FooterLinks.js
@@ -9,6 +9,10 @@ require('./FooterLinks.css');
 type State = {| hide: boolean |};
 
 class FooterLinks extends PureComponent<{||}, State> {
+  _onClick = () => {
+    this.setState({ hide: true });
+  };
+
   constructor() {
     super();
     this.state = {
@@ -26,7 +30,7 @@ class FooterLinks extends PureComponent<{||}, State> {
           aria-label="Hide links to legal information"
           title="Hide links to legal information"
           className="appFooterLinksClose"
-          onClick={() => this.setState({ hide: true })}
+          onClick={this._onClick}
         >
           ✕
         </button>
diff --git a/src/components/app/Home.js b/src/components/app/Home.js
index 5bed2a8842..67cb09ba3e 100644
--- a/src/components/app/Home.js
+++ b/src/components/app/Home.js
@@ -19,6 +19,15 @@ const ADDON_URL =
 const LEGACY_ADDON_URL =
   'https://raw.githubusercontent.com/devtools-html/Gecko-Profiler-Addon/master/gecko_profiler_legacy.xpi';
 
+function onInstallClick(e: SyntheticEvent<HTMLAnchorElement>) {
+  if (window.InstallTrigger) {
+    const name = e.currentTarget.dataset.name;
+    const xpiUrl = e.currentTarget.href;
+    window.InstallTrigger.install({ [name]: xpiUrl });
+  }
+  e.preventDefault();
+}
+
 const InstallButton = ({
   name,
   xpiUrl,
@@ -29,12 +38,8 @@ const InstallButton = ({
     <a
       href={xpiUrl}
       className={className}
-      onClick={e => {
-        if (window.InstallTrigger) {
-          window.InstallTrigger.install({ [name]: xpiUrl });
-        }
-        e.preventDefault();
-      }}
+      data-name={name}
+      onClick={onInstallClick}
     >
       {children}
     </a>
@@ -54,6 +59,7 @@ type UploadButtonProps = {
 
 class UploadButton extends React.PureComponent<UploadButtonProps> {
   _input: HTMLInputElement | null;
+  _takeInputRef = input => (this._input = input);
 
   constructor(props: UploadButtonProps) {
     super(props);
@@ -63,13 +69,7 @@ class UploadButton extends React.PureComponent<UploadButtonProps> {
   render() {
     return (
       <div>
-        <input
-          type="file"
-          ref={input => {
-            this._input = input;
-          }}
-          onChange={this._upload}
-        />
+        <input type="file" ref={this._takeInputRef} onChange={this._upload} />
       </div>
     );
   }
diff --git a/src/components/calltree/CallTree.js b/src/components/calltree/CallTree.js
index 343da8ec65..52a38fb2d8 100644
--- a/src/components/calltree/CallTree.js
+++ b/src/components/calltree/CallTree.js
@@ -60,6 +60,7 @@ class CallTreeComponent extends PureComponent<Props> {
   _appendageColumn: Column;
   _appendageButtons: string[];
   _treeView: TreeView | null;
+  _takeTreeViewRef = treeView => (this._treeView = treeView);
 
   constructor(props: Props) {
     super(props);
@@ -188,9 +189,7 @@ class CallTreeComponent extends PureComponent<Props> {
         disableOverscan={disableOverscan}
         appendageButtons={this._appendageButtons}
         onAppendageButtonClick={this._onAppendageButtonClick}
-        ref={ref => {
-          this._treeView = ref;
-        }}
+        ref={this._takeTreeViewRef}
         contextMenuId={'ProfileCallTreeContextMenu'}
         icons={this.props.icons}
       />
diff --git a/src/components/header/ThreadStackGraph.js b/src/components/header/ThreadStackGraph.js
index 74f4c58592..56afb24ab2 100644
--- a/src/components/header/ThreadStackGraph.js
+++ b/src/components/header/ThreadStackGraph.js
@@ -10,6 +10,8 @@ import { getSampleCallNodes } from '../../profile-logic/profile-data';
 import { BLUE_70, BLUE_40 } from 'photon-colors';
 
 class ThreadStackGraph extends PureComponent {
+  _takeCanvasRef = canvas => (this._canvas = canvas);
+
   constructor(props) {
     super(props);
     this._resizeListener = () => this.forceUpdate();
@@ -146,7 +148,7 @@ class ThreadStackGraph extends PureComponent {
             `${this.props.className}Canvas`,
             'threadStackGraphCanvas'
           )}
-          ref={ref => (this._canvas = ref)}
+          ref={this._takeCanvasRef}
           onMouseUp={this._onMouseUp}
         />
       </div>
diff --git a/src/components/marker-table/index.js b/src/components/marker-table/index.js
index 90b810b448..1e32969168 100644
--- a/src/components/marker-table/index.js
+++ b/src/components/marker-table/index.js
@@ -115,6 +115,8 @@ class MarkerTree {
 }
 
 class MarkerTable extends PureComponent {
+  _takeTreeViewRef = treeView => (this._treeView = treeView);
+
   constructor(props) {
     super(props);
     this._fixedColumns = [
@@ -155,7 +157,7 @@ class MarkerTable extends PureComponent {
           onExpandedNodesChange={this._onExpandedNodeIdsChange}
           selectedNodeId={selectedMarker}
           expandedNodeIds={this._expandedNodeIds}
-          ref={ref => (this._treeView = ref)}
+          ref={this._takeTreeViewRef}
           contextMenuId={'MarkersContextMenu'}
         />
       </div>
diff --git a/src/components/shared/IdleSearchField.js b/src/components/shared/IdleSearchField.js
index 1e7919b3fc..bd8ba0b9fc 100644
--- a/src/components/shared/IdleSearchField.js
+++ b/src/components/shared/IdleSearchField.js
@@ -97,6 +97,10 @@ class IdleSearchField extends PureComponent<Props, State> {
     }
   }
 
+  _onFormSubmit(e: SyntheticEvent<HTMLFormElement>) {
+    e.preventDefault();
+  }
+
   componentWillReceiveProps(nextProps: Props) {
     if (nextProps.defaultValue !== this.props.defaultValue) {
       this._notifyIfChanged(nextProps.defaultValue || '');
@@ -111,7 +115,7 @@ class IdleSearchField extends PureComponent<Props, State> {
     return (
       <form
         className={classNames('idleSearchField', className)}
-        onSubmit={e => e.preventDefault()}
+        onSubmit={this._onFormSubmit}
       >
         <input
           type="search"
diff --git a/src/components/shared/TreeView.js b/src/components/shared/TreeView.js
index 10fc29ae6e..0750687e66 100644
--- a/src/components/shared/TreeView.js
+++ b/src/components/shared/TreeView.js
@@ -282,6 +282,7 @@ class TreeView extends React.PureComponent<TreeViewProps> {
   _specialItems: (IndexIntoCallNodeTable | null)[];
   _visibleRows: IndexIntoCallNodeTable[];
   _list: VirtualList | null;
+  _takeListRef = (list: VirtualList | null) => (this._list = list);
 
   constructor(props: TreeViewProps) {
     super(props);
@@ -556,9 +557,7 @@ class TreeView extends React.PureComponent<TreeViewProps> {
             specialItems={this._specialItems}
             disableOverscan={disableOverscan}
             onCopy={this._onCopy}
-            ref={ref => {
-              this._list = ref;
-            }}
+            ref={this._takeListRef}
           />
         </ContextMenuTrigger>
         {contextMenu}
diff --git a/src/components/shared/chart/Viewport.js b/src/components/shared/chart/Viewport.js
index cb0481c329..ac8d82899e 100644
--- a/src/components/shared/chart/Viewport.js
+++ b/src/components/shared/chart/Viewport.js
@@ -116,7 +116,8 @@ export default function withChartViewport<Props: ViewportProps>(
     shiftScrollId: number;
     zoomRangeSelectionScheduled: boolean;
     zoomRangeSelectionScrollDelta: number;
-    _container: ?HTMLElement;
+    _container: HTMLElement | null;
+    _takeContainerRef = container => (this._container = container);
 
     constructor(props: Props) {
       super(props);
@@ -131,6 +132,7 @@ export default function withChartViewport<Props: ViewportProps>(
       this.shiftScrollId = 0;
       this.zoomRangeSelectionScheduled = false;
       this.zoomRangeSelectionScrollDelta = 0;
+      this._container = null;
 
       this.state = this.getDefaultState(props);
     }
@@ -477,9 +479,7 @@ export default function withChartViewport<Props: ViewportProps>(
           className={viewportClassName}
           onWheel={this._mouseWheelListener}
           onMouseDown={this._mouseDownListener}
-          ref={container => {
-            this._container = container;
-          }}
+          ref={this._takeContainerRef}
         >
           <WrappedComponent
             {...this.props}
diff --git a/src/test/.eslintrc.json b/src/test/.eslintrc.json
index 1ba62115c9..250609a9b1 100644
--- a/src/test/.eslintrc.json
+++ b/src/test/.eslintrc.json
@@ -1,6 +1,9 @@
 {
   "env": {
-      "jest": true
-    }
+    "jest": true
+  },
+  "rules": {
+    "react/jsx-no-bind": 0
+  }
 }
 
diff --git a/src/test/components/__snapshots__/Home.test.js.snap b/src/test/components/__snapshots__/Home.test.js.snap
index bbf79dfd7f..b9a43c9517 100644
--- a/src/test/components/__snapshots__/Home.test.js.snap
+++ b/src/test/components/__snapshots__/Home.test.js.snap
@@ -231,6 +231,7 @@ exports[`app/Home renders the install screen for the extension 1`] = `
           </p>
           <a
             className="homeSectionInstallButton"
+            data-name="Gecko Profiler"
             href="https://raw.githubusercontent.com/devtools-html/Gecko-Profiler-Addon/master/gecko_profiler.xpi"
             onClick={[Function]}
           >
@@ -386,6 +387,7 @@ exports[`app/Home renders the install screen for the legacy add-on 1`] = `
              
             <a
               className={undefined}
+              data-name="Gecko Profiler"
               href="https://raw.githubusercontent.com/devtools-html/Gecko-Profiler-Addon/master/gecko_profiler_legacy.xpi"
               onClick={[Function]}
             >
diff --git a/yarn.lock b/yarn.lock
index c89ad473d7..c3a8414117 100644
--- a/yarn.lock
+++ b/yarn.lock
@@ -593,6 +593,10 @@ babel-plugin-syntax-async-functions@^6.8.0:
   version "6.13.0"
   resolved "https://registry.yarnpkg.com/babel-plugin-syntax-async-functions/-/babel-plugin-syntax-async-functions-6.13.0.tgz#cad9cad1191b5ad634bf30ae0872391e0647be95"
 
+babel-plugin-syntax-class-properties@^6.8.0:
+  version "6.13.0"
+  resolved "https://registry.yarnpkg.com/babel-plugin-syntax-class-properties/-/babel-plugin-syntax-class-properties-6.13.0.tgz#d7eb23b79a317f8543962c505b827c7d6cac27de"
+
 babel-plugin-syntax-exponentiation-operator@^6.8.0:
   version "6.13.0"
   resolved "https://registry.yarnpkg.com/babel-plugin-syntax-exponentiation-operator/-/babel-plugin-syntax-exponentiation-operator-6.13.0.tgz#9ee7e8337290da95288201a6a57f4170317830de"
@@ -621,6 +625,15 @@ babel-plugin-transform-async-to-generator@^6.22.0:
     babel-plugin-syntax-async-functions "^6.8.0"
     babel-runtime "^6.22.0"
 
+babel-plugin-transform-class-properties@^6.24.1:
+  version "6.24.1"
+  resolved "https://registry.yarnpkg.com/babel-plugin-transform-class-properties/-/babel-plugin-transform-class-properties-6.24.1.tgz#6a79763ea61d33d36f37b611aa9def81a81b46ac"
+  dependencies:
+    babel-helper-function-name "^6.24.1"
+    babel-plugin-syntax-class-properties "^6.8.0"
+    babel-runtime "^6.22.0"
+    babel-template "^6.24.1"
+
 babel-plugin-transform-es2015-arrow-functions@^6.22.0:
   version "6.22.0"
   resolved "https://registry.yarnpkg.com/babel-plugin-transform-es2015-arrow-functions/-/babel-plugin-transform-es2015-arrow-functions-6.22.0.tgz#452692cb711d5f79dc7f85e440ce41b9f244d221"
@@ -2354,6 +2367,10 @@ eslint-module-utils@^2.1.1:
     debug "^2.6.8"
     pkg-dir "^1.0.0"
 
+eslint-plugin-babel@^4.1.2:
+  version "4.1.2"
+  resolved "https://registry.yarnpkg.com/eslint-plugin-babel/-/eslint-plugin-babel-4.1.2.tgz#79202a0e35757dd92780919b2336f1fa2fe53c1e"
+
 eslint-plugin-flowtype@^2.39.1:
   version "2.39.1"
   resolved "https://registry.yarnpkg.com/eslint-plugin-flowtype/-/eslint-plugin-flowtype-2.39.1.tgz#b5624622a0388bcd969f4351131232dcb9649cd5"