I say remove the word "CTO" or any other 3-letter acronym that starts with C from your lexicon for now. Can he be your partner -- that is, can you depend on him and be open and honest with him?
> told me he had watched the Social Network last night, and it made him want to work on this with me
Yikes.
Him watching the Social Network and being motivated from that is slightly worrisome to me as well, but it was a movie that even with it being mostly fictitious, it still showed the possibility of success in Silicon Valley.
It's your own choice, but if you can't depend on him, doesn't have the skills in the areas he'd need to have, and seemingly wants to muscle in because he's watched a movie, then I think it's probably better if you find a way to decline without being too rude about it.
Maybe help brainstorm his own idea he can run with, if only to be supportive?