Is it possible to delete a message I wrote in the chat?
You can't completely delete a message, but you can edit it down to (nearly) nothing if you are within 5 minutes of posting. As of now (June 2020), you have one further option: you can flag your own message. This will:
* make it immediately invisible to anyone who isn't logged in
* potentially draw the attention of one of the flag crew (though they don't get notifications about chat flags, so it's a case of whether they happen to be in the room or if you ping them). If one of the flag crew adds their own flag, the message becomes invisible to everyone (except you and the flag crew).
There should be a way to delete chat messages, and we will add this and update this answer when we do.
There will ultimately be a 'comments/chat cleanup crew' to complement the '[post cleanup crew](/meta?q=182#a402)', and they will be able to see deleted messages as they may be necessary to interpret flags.
I think perhaps deleted messages should remain visible (but be clearly marked as deleted) for those currently in the chat room — they can disappear properly on refresh or navigation.
It sure doesn't look like it.
Maybe the same red "close" button as used to dismiss messages can appear in the same location on one's own messages until edit time runs out?
I also propose that if one edits a chat message before time runs out, removing all of its content, it should disappear. Currently, one just cannot submit it if it is all whitespace.