Sure, pigs may turn into flying unicorns before this ever happens, but hey ... that's why we're dreaming, right? Halo is easily Microsoft's largest franchise, and it would make a perfect home on PSP. The FPS game has you playing as Master Chief, a soldier in a war against "The Flood," and became one of the single best reasons to own the original Xbox.
A portable version was considered by Microsoft, but for a much less capable platform: the DS. The PSP, with its much more impressive tech, would be able to handle the processing needs of a Halo title much better. FPS controls haven't been perfected on the system yet, but that certainly didn't stop Goldeneye from becoming so popular back in the single analog stick era. A version of Halo for the portables would be well-suited for the older, hardcore PSP community, in either a FPS, or Halo Wars-style RTS game. Also, online would be a bit more fun without those silly friend codes. Unless Microsoft is making a portable Xbox, Sony's handheld is where they can go to cash in the big bucks.
Is it possible?
No. Even though it would make a ton of money, it will most likely never happen.