We report the first measurement of the energy gap of the high-temperature bismuth oxide superconductor Ba0.6K0.4BiO3 (Tc30 K). With temperature- and magnetic-field-dependent infrared reflectivity measurements, we obtain a reduced energy gap of 2/kTc3.50.5, consistent with a BCS-type mechanism with moderate or weak coupling. In the normal state a broad peak in the infrared conductivity is observed near 5000 cm-1. This unusual infrared behavior is common to both the BaPb1-xBixO3 and the Ba1-xKxBiO3 systems and may provide a fundamental clue to the mechanism of superconductivity in the cubic bismuth oxides. © 1989 The American Physical Society.