The elimination of defects from SiC has facilitated its move to the forefront of the optoelectronics and power-electronics industries. Nonetheless, because certain SiC defects have electronic states with sharp optical and spin transitions, they are increasingly recognized as a platform for quantum information and nanoscale sensing. Here, we show that individual electron spins in high-purity monocrystalline 4H-SiC can be isolated and coherently controlled. Bound to neutral divacancy defects, these states exhibit exceptionally long ensemble Hahn-echo spin coherence times, exceeding 1 ms. Coherent control of single spins in a material amenable to advanced growth and microfabrication techniques is an exciting route towards wafer-scale quantum technologies.