The high density of heat generated in power electronics and optoelectronic devices is a critical bottleneck in their application. New materials with high thermal conductivity are needed to effectively dissipate heat and thereby enable enhanced performance of power controls, solid-state lighting, communication, and security systems. We report the experimental discovery of high thermal conductivity at room temperature in cubic boron arsenide (BAs) grown through a modified chemical vapor transport technique. The thermal conductivity of BAs, 1000 +/- 90 watts per meter per kelvin meter-kelvin, is higher than that of silicon carbide by a factor of 3 and is surpassed only by diamond and the basal-plane value of graphite. This work shows that BAs represents a class of ultrahigh thermal conductivity materials predicted by a recent theory, and that it may constitute a useful thermal management material for high-power density electronic devices.