Semiconducting cubic boron arsenide (c-BAs) has been predicted to have carrier mobility of 1400 square centimeters per volt-second for electrons and 2100 square centimeters per volt-second for holes at room temperature. Using pump-probe transient reflectivity microscopy, we monitored the diffusion of photoexcited carriers in single-crystal c-BAs to obtain their mobility. With near-bandgap 600-nanometer pump pulses, we found a high ambipolar mobility of 1550 ± 120 square centimeters per volt-second, in good agreement with theoretical prediction. Additional experiments with 400-nanometer pumps on the same spot revealed a mobility of >3000 square centimeters per volt-second, which we attribute to hot electrons. The observation of high carrier mobility, in conjunction with high thermal conductivity, enables an enormous number of device applications for c-BAs in high-performance electronics and optoelectronics.