This is an simple and easy resource to toggle on and off the FiveM chat for yourself. Note: You won't get any messages, but other players could possible see your messages.
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Download the resource and replace it with the chat resource from FiveM. Note: If you have any changes made in your chat resource, note that they will get overwrited.
Turn your chat off with /togglechat off and turn it on again with /togglechat on