I don't have Facebook.
What do they say about the status of their "Chat" servers ?
If you are using an SSL Login try it without.
If you are not try it with an SSL Login.
Please, if posting Logs, do not post any Log info after the line "Binary Images for iChat"
iMac 2.5Ghz 5i 2011 (Mountain Lion 10.8.2)
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
"Limit the Logs to the Bits above Binary Images." No, Seriously
I had the same issue, but I just solved it possibly. My problem was that when I upgraded from Snow Leopard to Mountain Lion, it messed with the settings for my Facebook account for some reason. Make sure you have it set to find ports automatically. This is what I now have in the settings automatically detected, and it works fine for now:
Use SSL: false
Use Kerberos v5 for authentication: false