What do you mean by chat, Twitch chat or ingame chat? It sounds like you mean the ingame chat, which shouldn't be that big of a deal as a bot already exists as imlegos mentioned. The problem we were discussing before was deleting messages of Twitch chat, which seems to be possible only in a not very satisfactorily way.
Twitch vs client
I recently played Multiplayer with a friend of mine and noticed that you can set a client to spectator mode where he can not build. So some sort of user system is already implemented, my idea would be to add an access level where they only could control peeps (or only their personal peep respectively) and chat. Then again spectator access should be just fine for the job anyway, as spectators are allowed to chat, aren't they? So this only would be required if you implement some new gui feature (or an other non chat solution) for controlling the peep.
With an client approach you could watch your peep move through the park opposed to the Twitch way. Also with the client approach you are able to manipulate chat the way you want it. But that way the engine would have to assign a peep to the client manually, different from Twitch were the user is limited by his user name. But one does not have to cancel out the other, once one way is implemented the other one shouldn't be to hard to implement either. I guess it would be wise to implement the easier one (Twitch I assume) first and see if the other one is really necessary.
Groups
Groups are an interesting idea! However considering the level of complexity it would probably be more viable to implement this feature by itself before introducing it to the player controlled peep system which in itself has to be actually implemented. One step at a time
We are constructing a solid idea here. Gotta sum up all the ideas coming from you, maybe put it into the wiki and discuss with the developers what their standpoint on this is