iChat has been going in one form or another since 2001
The Apple IDs over that period have Changed several times from the methods that Preceded the .Mac (dot Mac) service (@mac.com names) and then the MobileMe (@me.com names) that followed that to the current iCloud ones (also @me.com names)
Other forms of Apple ID such as names create at Apple without email, those created with external to Apple emails (@Yahoo.com or @hotmail.com or ISPs emails) are not Valid AIM names that the @mac and @me.com ones are.
Currently iCloud does allow you to link a new iCloud Issued @me.com name to an existing Apple ID
You then effective get two names to your Apple ID.
The @me.com name will only work in iChat 6 though as these require a login to me.com to allow AIM to verify the Password.
Register a new name at AIM (you can use an Existing email if you wish)
If you create an AIM name it looks like it will be an Email but only the first (Username) part is used for Chatting.
You can create as many AIM names with a Recovery email as you wish.
You can create another Apple ID with an @mac.com ending
At one time these were billed as "iChat Names"
1) You CANNOT create a second Apple ID with an Email that is or is used with another Apple ID (So if your current Apple ID is based on an email you can't use that to create an @mac.com name)
2) Although the page does not tell you, you will need to keep the password to 16 characters or less to work with the AIM servers.
Unfortunately not all Apple IDs are equal.
Please, if posting Logs, do not post any Log info after the line "Binary Images for iChat"
iMac 2.5Ghz 5i 2011 (Lion 10.7.2)
G4/1GhzDual MDD (Leopard 10.5.8)
MacBookPro 2Gb (Snow Leopard 10.6.8)
Mac OS X (10.6.8),
"Limit the Logs to the Bits above Binary Images." No, Seriously