We report observation of Bose-Einstein condensation (BEC) of a trapped, dilute gas of atomic hydrogen. The condensate and normal gas are studied by two-photon spectroscopy of the 1S- 2S transition. Interactions among the atoms produce a shift of the resonance frequency proportional to density. The condensate is clearly distinguished by its large frequency shift. The peak condensate density is 4.8+/-1.1×1015 cm-3, corresponding to a condensate population of 109 atoms. The BEC transition occurs at about T = 50 μK and n = 1.8×1014 cm-3.