Not really enough info to help constructively.
Which Version of iChat ?
Is it iChat to iChat or iChat to Messages (i.e Mac to Mac) or AIM (iChat) to PC AIM (needs to be a compatible version)
Is this AIM to AIM (Includes AIM valid Screen Names from certain Apple IDs) ?
Is it Jabber to Jabber (this can only be done Mac to Mac in Messages and/or iChat) ?
Do you get any failure message ?
In the Video Menu > Connection Doctor > Errors tab do you get any info ?
As mentioned it is iChat to iChat or iChat to AIM on a PC if the PC has a compatible version (which is not the latest) (where it lists iChat it also means Messages in Mountain Lion)
It has to be either AIM to AIM IDs or Jabber to Jabber IDs
It cannot be Jabber to some GoogleTalk Web Browser Login (or Facebook)
It cannot be Jabber/Google Talk to the PC app called GoogleTalk
Google released an PC only App that will use Jabber protocols for Video (Called Jingle)
Their web Browser Plug-in also uses Jingle for Video and Audio chat but iChat and Messages use SIP (Session Initiation Protocol) to connect. The two are not compatible.
Facebook also run a Jabber server and have apparently released their Own Plug-in which can cause problems of it's own on a Mac.
However you also cannot video to a Web Browser Login on Mac or PC
If this is iChat 6 it does not Video on the Yahoo Accounts (that is Text Only)
This means it cannot Video to any version of Yahoo on Mac or PC or any Web Browser method.
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