Hi,
AIM allow several non AIM registered names/IDs as valid Screen Names.
In the case of Apple this includes @mac.com Names (All whether they are still in use, were trail account with Apple originally or are lapsed paid for accounts).
Any @me.com that has been linked to iCloud to keep it active. (MobileMe di have Trial Accounts but you had to manually close them before being charged if you di not want them. Lapsed paid for ones also no longer work as Apple IDs and therefore don't work as AIM Screen Names as well).
Any iCloud linked account. This could be an @me.com name or @icloud.com names that were issued later.
These will all work on Messages only and the last version of iChat 6.
The update to iChat was where the check with Apple Server AND the AIM servers at the same time was started to check the Login is valid.
This means all these no longer work in iChat 1 through 5 and the earlier version of iChat 6 as these versions only rely on logging into AIM and the AIM server checking the Apple Servers only which is no longer allowed.
My First reply back on July 14th had already mentioned your solution when the Original Poster then cam back and said they were using an @mac.com name.

8:36 pm Thursday; November 5, 2015
iMac 2.5Ghz i5 2011 (Mavericks 10.9)
G4/1GhzDual MDD (Leopard 10.5.8)
MacBookPro 2Gb (Snow Leopard 10.6.8)
Mac OS X (10.6.8),
Couple of iPhones and an iPad