We show that there is a calculable upper limit on the mass of the lightest Higgs boson in any supersymmetric theory that remains perturbative up to a high scale . There are no restrictions on the Higgs sector, or the gauge group or particle content. We estimate the value of the upper limit to be mh◦ < 146 GeV for 100 GeV <∼ Mt <∼ 145 GeV, from all effects except possibly additional heavy fermio...