There wasn't even a Halo game as a launch title, but there was backwards support for the original Xbox Halo games on the 360.

https://en.wikipedia.org/wiki/Xbox_360_launch#Titles

There wouldn't be a Halo game released for the Xbox 360 until September 2007, nearly two years after the release of the console.

I tie Halo IP to PS3/360 calculation because at the time of Xbox 360 - Halo became a major IP for Xbox. If you want to play new Halo with friends - you need an Xbox 360.