You do, unless the company happens to be pretty well connected (think Google, Apple). Then they can get you a visa which might not be H1-B but you get the same "benefits".
H1-B requires 4 year bachelor or 3 years of professional experience in the relevant field for each missing academic year. The only other working visa I can think of is the O-1, which is given to "outstanding individuals", which basically means high profile researchers, world renown designers etc.
