As has already been pointed out Mountain Lion has Messages instead of iChat.
It is built one the iChat engine and will do everything that iChat can do PLUS the iMessages bit via the new(ish) Apple Messaging service called iMessages with iOS devices using either Apple IDs or iPhone numbers.
I presume you have set up an iMessage account in Messages by "registering" an Apple ID with the server.
If you open the App and click on the Messages Menu > Preferences > Accounts there should be at least two accounts listed - the iMessages one and the Bonjour one (everyone gets Bonjour)
You will notice that there is a + icon button below the list on the left.
In the new pane you will find the top item is a drop down.
In Messages it offers you the chance to create an AIM, Jabber or GoogleTalk account or a Yahoo one.
You need to have either a Screen Name that works with the AIM service, a Jabber ID (which could be a GoogleTalk ID) or a Yahoo ID.
As Apple have an agreement with AIM that Apple IDs issued by Apple can be valid AIM screen Names you may already have a email that can double as an AIM name as well as the iMessages ID.
It needs to end with either @mac.com (from the .Mac Service Days) or @me.com and @icloud.com after being issued by iCloud.
If you migrated or Upgraded a computer to Mountain Lion then you may have IDs or names in System Preferences > Mail, Contacts and Calendars that can be Activated for Messages.
Once you have either activated an ID is Systems Preferences or Added it directly in Messages then it can be seen in the Window menu of the App (see "Buddies" CMD + 1)
This will then display a combined Buddy List.
If the app is closed with the Buddy List on show then it will be on show the next time the app is opened.
The Buddy lists can actually be separated by unticking the line about Gathering all Accounts in to one list in the General Section of the Preferences.
A Buddy list that has had Buddies added to it will display the familiar green Video and Audio Only icons.
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