Optical gyroscopes are among the most accurate rotation measuring devices and are widely used for navigation and accurate pointing. Since the advent of photonic integrated components for communications, and with their increasing complexity, there has been interest in the possibility of chip-scale optical gyroscopes. Besides the potential benefits of integration, such solid-state systems would be robust and resistant to shock. Here, we report a gyroscope using Brillouin ring lasers on a silicon chip. Its stability and sensitivity enable measurement of Earth’s rotation, representing a major milestone for this new class of gyroscope.