Semiconductors with high thermal conductivity and electron-hole mobility are of great importance for electronic and photonic devices as well as for fundamental studies. Among the ultrahigh-thermal conductivity materials, cubic boron arsenide (c-BAs) is predicted to exhibit simultaneously high electron and hole mobilities of >1000 centimeters squared per volt per second. Using the optical transient grating technique, we experimentally measured thermal conductivity of 1200 watts per meter per kelvin and ambipolar mobility of 1600 centimeters squared per volt per second at the same locations on c-BAs samples at room temperature despite spatial variations. Ab initio calculations show that lowering ionized and neutral impurity concentrations is key to achieving high mobility and high thermal conductivity, respectively. The high ambipolar mobilities combined with the ultrahigh thermal conductivity make c-BAs a promising candidate for next-generation electronics.