Some friends and I plan to start a corporation in California. Because we will have three shareholders, we believe we need to have three directors. The problem is that two of the three shareholders are H-1B visa holders. Is there a way that we can appoint only one director and still have three shareholders?
You've done the math right: A California for-profit corporation with three or more shareholders needs three or more directors unless no shares have been issued. (But you will likely want to issue shares to perfect the organization of your corporation.)
California law places no restrictions on who may be directors. So unless your bylaws imposed an added requirement, the visa status of your shareholders is not a problem by itself.
However, the H-1B status of your shareholders may be a problem if your corporation has elected S corporation tax status (meaning that it is taxed like a partnership). That's because non-permanent residents (such as H-1B visa holders) may not own the shares of an S corporation. If they do, your corporation could lose its S corporation status, so check with your tax advisor.