This has been suggested and turned down so many times. Why?
How it works
Have a command like /ignore [username] and /unignore [username] or something like a x beside a person's username. Once activated, you cannot see that users posts. Simple. For people who haven't ignored that user, they can still see them chat. You can have the option to tell the person that you've been ignored. But either way, if the person hasnt ignored you and you have, the person can still see you chat, so I guess you could tell the person that way.
PROS
~ Annoying ass users can technically be kicked without having to have a moderator there.
~ If you want peace and quiet, this can be the tool to use.
~ If you just really dislike/never get along with someone, this is the tool for you.
~ You cannot ignore authority, so then they will be able to enforce rules.
Cons
~ People can miss parts of the chat, but it's on them for ignoring that user. Its not big of a deal anyways.
~ It can cause feuds off chat.