Use the !block command to prevent a troublesome visitor from messaging you. A block lasts for 24 hours (or until the visitor clears their browser cookies,) after which time they can message you again. The visitor will NOT receive any indication that they've been blocked or that the block has cleared.

If you need a more permanent block, try setting up a Targeted Chat rule to hide the chat box from a particular IP address. You can find a visitor's IP address in the Advanced Info section at the bottom of every chat transcript.