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Conventional theory predicts that ultrahigh lattice thermal conductivity can only occur in crystals composed of strongly bonded light elements, and that it is limited by anharmonic three-phonon processes. We report experimental evidence that departs from these long-held criteria. We measured a local room-temperature thermal conductivity exceeding 1000 watts per meter-kelvin and an average bulk value reaching 900 watts per meter-kelvin in bulk boron arsenide (BAs) crystals, where boron and arsenic are light and heavy elements, respectively. The high values are consistent with a proposal for phonon-band engineering and can only be explained by higher-order phonon processes. These findings yield insight into the physics of heat conduction in solids and show BAs to be the only known semiconductor with ultrahigh thermal conductivity.