Microsoft tried Intel in the Xbox Gen 1.  Microsoft tried IBM in the Xbox 360.

Now Microsoft has decided to just make their own microprocessor for the next generation Xbox.  As quoted from Engadget:

"According to a report in yesterday's Gray Lady, Microsoft will be starting its own chip design division, with the ultra-creative name: "The Computer Architecture Group," and will be split between Redmond, Washington and Mountain View, California. The venerable NYT adds that Microsoft will use the lab to beef up chips in the next-generation Xbox (the Xbox 720?), and will be headed by Charles P. Thacker. He's formerly of the legendary Xerox Palo Alto Research Center, where he helped work on the original Alto and the invention of Ethernet."