I'm on H1B with a university. I want to start a company. My university is ok with me doing it on the side. Can I do it being on H1B?

You can start a company while on an h1b, but you cannot work there unless you get an independent visa. You may invest and get an E2 visa.  This depends on your nationality. Feel free to email me your nationality and approximate investment. Here is some additional information. The investor, either a real or corporate person, must be a national of a treaty country; The investment must be substantial. It must be sufficient to ensure the successful operation of the enterprise. The percentage of investment for a low-cost business enterprise must be higher than the percentage of investment in a high-cost enterprise; The investment must be a real operating enterprise. Speculative or idle investment does not qualify. Uncommitted funds in a bank account or similar security are not considered an investment; The investment may not be marginal. It must generate significantly more income than just to provide a living to the investor and family, or it must have a significant economic impact in the United States; The investor must have control of the funds, and the investment must be at risk in the commercial sense. Loans secured with the assets of the investment enterprise are not allowed; and The investor must be coming to the U.S. to develop and direct the enterprise. If the applicant is not the principal investor, he or she must be employed in a supervisory, executive, or highly specialized skill capacity. Ordinary skilled and unskilled workers do not qualify.