Have a normal but CSR-controlled character logged on at all times. Wait for the spam. Ban the account.
Park the character next to a mailbox so you can check that. If general chat spam is your problem, go wherever that is most common (say Bree-town). You do not even need to pay attention much: look every five minutes and do a round of bans. Internship opportunity! Some games must already be doing this, but I want to mention it since it would help with quick response to spammers.