Superconductor-insulator-superconductor tunnel junctions have been fabricated on MgB2 that display Josephson and quasiparticle currents. These junctions exhibit a gap magnitude, Delta~2.5 meV, that is considerably smaller than the BCS value, but which clearly and reproducibly closes near the bulk Tc. In conjunction with fits of the conductance spectra, these results are interpreted as direct evidence of two-band superconductivity.