I played Chaos Theory back when it came out on the PS2, and really liked it. I felt like going back and revisiting it a while ago and wound up buying a digital copy for PC from Ubi's online store.

The problem is that it absolutely refuses to run in Windows 7, under any permutation of compatibility settings. The best I can do is sometimes get it to load to the main menu, but I can never get farther than that.

I've tried Google, and it looks like (stupidly) the only real solution is to find cracks and grey market patches for a game I legitimately bought.

I guess I'll do it if I have to, but I did pay for this and I'd like it to work as intended. Has anybody found a not-terrible solution to get this running in Win7?

I'm with you on that, Chaos Theory is still the best Splinter Cell game in my opinion, but onto your question. 
 
From what I recall the PC version came with some messed up stuff (cough... DRM cough...) and it doesn't play nice with win 7, or any PC for that matter. Do the usual PC trouble shooting stuff first, like updating your video drivers and trying a reinstall of the game. If none of that works, contact Ubisoft support see what they can do for you, otherwise the steam forums for the Tom Clancy Collections may have your problem addressed there.  Posting some of your PC specs is always helpful too.