Sure you could! I used XNA Game Studio to produce games and apps that would run on my 360. They couldn't take full advantage of the hardware. But if you paid

Sure you could! I used XNA Game Studio to produce games and apps that would run on my 360. They couldn't take full advantage of the hardware. But if you paid a fee, you could sell your game on XBL much like the App Store or Steam. https://en.wikipedia.org/wiki/Microsoft_XNA_Game_Studio https://en.wikipedia.org/wiki/Microsoft_XNA_Game_Studio