Can I open a business on H1B visa?
In the United States, just about anyone in the world may register an LLC or a Corporation without having to be a citizen, resident or even present in the country. You are not required to have a U.S. address for the business, or submit any identification or financial documents, so you would not require any type of visa to be incorporated.
With that being said, various visas come with various terms and restrictions, and I believe H1B has its own share of both. Since we are not experts in immigration law I would recommend you to consult an immigration attorney or visit USCIS website and see what are those restrictions.
I'd like to invite you to read our research article titled 'U.S. Companies for Foreigners'. I believe you will find many helpful answers to common questions regarding registering your business in the United States.