It's unclear whether the OP is asking "Can I found a US company and then move to the US to work on that company via the company applying for an H1B visa for me?", or "Can I, currently in the US on an H1B visa, start a new company and work for it?". I suspect the answer to the latter question is "no". The rest of this comment assumes the former question.
As others here have said, an H1B visa requires demonstrating that the company could fire you, which isn't usually true if you own it. In the case of Rapportive, we had 3 cofounders, all needing visas; 3 turns out to be the perfect number for H1B purposes, because any two of you own enough of the company to fire the third. That sounds a bit circular, but made enough sense to USCIS that we got our visas, even though none of us was a US citizen. (Not that it was easy, but our difficulties were more about convincing them we were a real company.)
Of course, this isn't legal advice, and you'll want a good immigration lawyer who can prepare the petition appropriately for this arrangement.
As others here have said, an H1B visa requires demonstrating that the company could fire you, which isn't usually true if you own it. In the case of Rapportive, we had 3 cofounders, all needing visas; 3 turns out to be the perfect number for H1B purposes, because any two of you own enough of the company to fire the third. That sounds a bit circular, but made enough sense to USCIS that we got our visas, even though none of us was a US citizen. (Not that it was easy, but our difficulties were more about convincing them we were a real company.)
Of course, this isn't legal advice, and you'll want a good immigration lawyer who can prepare the petition appropriately for this arrangement.