ATI is well positioned to be the supplier of graphics chips for Xbox 2 (or 'Xbox Next' if a recent MS domain registration is in any way prophetic) according to analysts at Dundee Securities.
Microsoft will be happy to encourage conflict between ATI and main rival NVIDIA over the positioning, because the two will now presumably engage in a war over who can produce the cheapest part. Expect the winner to appear in the next Xbox.
Of course ATI already supplies chips for Nintendo, so both companies are equally experienced in this area. The outcome of the next placement could potentially to come down to whose technology research cycle is further along.
Graphics isn't the only job up for grabs though. AMD and Intel are known to be sparring over the next CPU spot, and you can be sure Microsoft will flirt with just about anybody when it comes to filling the remaining gaps. Any resultant bidding wars can only benefit the platform holder's bottom line, and the console's eventual price tag.