It's called "Treaty Investing"

http://travel.state.gov/visa/temp/types/types_1273.html

Info on the E1 (trader) and E2 (investor) on the US Embassy in Mexico http://www.usembassy-mexico.gov/eng/evisas_E.html

Highlights for the investor visa: - The investor must be coming to the United States solely to develop and direct the enterprise - The investment must be substantial. It must be sufficient to ensure the successful operation of the enterprise - must have the capacity to generate significantly more income than just enough to provide a living to the investor and his or her family, or it must have a significant economic impact in the United States

I'm not sure if a YC funded founder would be elegible, but seems hard

I've been running my own business in the US on an E-2 visa for the last 12 years. The minimum recommended initial investment is of the order of $100,000 - and a majority the E-2 company must be owned by citizens of the non-US 'treaty country'.

Rough guide to application : 0.5-1.0 inch thick.

You have to bring $100,000 of your own personal money into the company (so investment from 3rd party doesn't count).

You also have to maintain control of your company, ie you can never give away more than 50% of the equity in the company - and that will be prohibitive when seeking investment.

The company is thus limited in it's ability to fundraise above a certain point and an exit is impossible without the founder leaving the country.

Forget about E*. Get simple b1/b2 - everyone qualify or L1-bit more complex but possible

Australians should take special interest in the E3 visa:

http://en.wikipedia.org/wiki/E-3_visa

I can imagine that incorporating a company in the US and then having that company sponsor you would be a valid use of the E3. Once the company has an LCA to prove a US resident can't do your job (requires some hoop jumping and waiting around), it's super easy to get the E3. For a really young/small company you'd probably need to go to some effort to prove that the company isn't simply a vehicle to get the visa for a foreigner.

I had an E3 and left of my own volition without applying for an extension. I tend to get a couple of minutes of extra questioning when going in to/transiting the US now, based on their assumption that I obviously want to return to live/work there, having experienced their awesomeness in the past. I know another person in exactly the same situation.

(edit: changed LMO -> LCA. I was confusing Canadian and US terminology)

From what I understand, you can't self-sponsor your visa as a single founder.

eg. You would still need a US co-founder. E1 or E2 may be a better visa to use if you don't have a co-founder.