don't think AOL software has that (at least it didn't when I used it)
use Trillian as the IM client instead. It has full logging, and lets you connect to multiple AIM, Yahoo, MSN, ICQ, etc. accounts (AND IRC) at the same time. They have a free and paid versions. Free one should be fine for most users. (no ads or spyware in it) http://www.trillian.cc