Most likely this is about the ports over the internet that iChat uses.
iChat uses 20 or more and up to 30 ports depending on version.
Some are used for AIM Logins, Jabber Logins and Bonjour traffic.
Others are used for A/V Chats
iChat 5 and earlier will use port 5190 to Log in to AIM (Although regular posters here have been suggesting using port 443 since iChat 2)
iChat 6 does use port 443 to Log in with.
Video and Audio Only Invites are sent out on port 5678
Even if your Mac Firewall is not set up for this Outgoing traffic is allowed.
The Connection process then moves to port 16402 as first choice if the Buddy hits Accept.
Most likely the issue is going to be you routing device.
The first 1024 ports are going to be opne by default
This allows Web Browsing on Port 80 (with secure logins on port 443) and Mail (Various ports) and some other apps to work "Out-of-the-Box"
The easiest method to use on modern router si UPnP if the device has it.
This is an ON/Off setting that allows the app to tell the router which and when the ports should be open.
In versions of ichat that can Screen Share it is important to use UPnP as Screen Sharing uses a Random port that cannot be opened by other methods.
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