I mistakenly used "ignore this user (everywhere)" in a chat room. How can I undo this?
There are several ways to do this.
Directly in the room
If the user is in a room with you (which is very likely if you just now ignored them), they'll not be totally hidden; their avatar in the user list in the top right has just shrunk:
If you click this small avatar, you can choose "don't ignore this user" in the resulting pop-up.
On your profile
When you go to your own chat user profile and click the "prefs" tab, this will take you to something like this:
(yours won't say "balpha", obviously). It shows a list of all users you're ignoring; just click the "X" on a user card to unignore.
On their profile
Go to the main chat page for your particular SO/SE site. For example http://chat.meta.stackoverflow.com/
At the very top you will find a link to the users.
Instead of "online" or "active", select the "all" tab. If you know the particular user's name, you can then filter users until you see the particular user you've ignored.
Clicking on this user's name will reveal a page specific to this user and a "don't ignore this user" button as illustrated below.
Clicking this will remove the user from your list of ignored users.