The first Halo was being developed for the personal computer (Mac to be precise) before it jumped ship onto the Xbox. A few years later post its release on the console, it eventually crawled onto the PC only to be met with a lukewarm reception from within the community. Halo 2 followed a similar suit and was tagged as being one of the first games to be available for Windows Vista. Halo 3 was rumored to fall in the footsteps along with its predecessors and make an appearance onto the platform, however it never did. There was no word on any development of the game on the platform.
This, however, might just be subject to change after you have a look at Matt Waggle’s profile who served as an object artist for Bungie Studios during the project. His duties included working on Bungie’s proprietary engine and building an effective collision and physics model on the basis of the Havok based physics engine. All these responsibilities were for Halo 3 which was being developed for the Xbox 360 and PC at that point in time. This gives an indication that the game was in fact in development for both platforms simultaneously.
No one ultimately knows what happened to the game for the PC especially since the developers started to focus their attention onto ODST and Halo: Reach currently. If we look at how things ultimately shaped up with Alan Wake we have to assume the development for the game was canceled to promote the resources for the Xbox 360 version so as to accommodate much more wholesome experience to its fans. One could also think of the fact that there were so many other first person shooters on the PC which would have made Halo 3 insipid when placed in direct comparison to them and hence Microsoft decided to cancel any further development of the game.