[tlb]

You can own and run a US business while on an H-1B. The H-1B is good as long as you're still employed by the sponsoring employer, and you can do pretty much whatever else you want while in the US on it.

Beware that your current employment probably has an "assignment of inventions" agreement, which may give them rights over software you create outside work. You can often negotiate an exception for a particular project.

If the startup starts growing and you want quit your existing job and to go full-time, it's more difficult but there may be options depending on your circumstances. You'll need a good immigration lawyer then.

[injb]

Are you sure about that? Can you cite some documentation/info from an immigration attorney? Most people out there seem to be under the impression that you can't do this. It's certainly the general rule that people on nonimmigrant visas can only work for the sponsoring employer.