Optical-based rotation sensors have revolutionized precision, high-sensitivity inertial navigation systems. At the same time these sensors use bulky optical fiber spools or free-space resonators. A chip-based, micro-optical gyroscope is demonstrated that uses counterpropagating Brillouin lasers to measure rotation as a Sagnac-induced frequency shift. Preliminary work has demonstrated a rotation-rate measurement that surpasses prior micro-optical rotation-sensing systems by over 40-fold. Inertial sensors for rotation are used widely in commercial and military systems. Driven by applications in consumer electronics and miniature satellites, there has been intense interest in compact, lightweight sensors that can be integrated with electronics. MEMS-based sensors have captured this miniature lightweight application space, but do not provide sensitivity and bias stability that competes with ring laser gyros [1] and fiber-optic gyros [2]. Moreover, due to their mechanical nature, MEMS-based devices are less immune to shock and vibration [3]. The prospect of applying micro-fabrication methods to optical-based gyro systems is therefore appealing, both because it addresses environmental concerns (even beyond conventional optical gyro systems) and it might offer performance that exceeds MEMS-based systems. A new class of micro-optical gyro is demonstrated that uses counterpropagating Brillouin lasers in a chip-based optical resonator to measure rotation as a frequency shift [4]. Preliminary work has measured sinusoidal rotations with rates as low as 22 deg/h, which surpasses prior experimental micro-optical systems by over 40-fold [5,6].A Brillouin laser ring gyro (BLRG) was studied in the 1990s using an optical fiber resonator [7]. Brillouin scattering in silica optical fiber results from the interaction of an optical pump wave with microwave-rate phonons [8]. At sufficiently high pump intensities, the process amplifies counterpropagating waves residing within a narrow frequency band (about 50 MHz wide) that is downshifted relative to the pump frequency by 10-11 GHz (for pumping near 1.55 μm). In a resonator, this amplification can overcome round-trip losses to produce a lasing Stokes wave. In the BLRG, a fiber ring resonator was bidirectionally pumped to excite two counterpropagating Brillouin lasers [7]. Upon rotation of the resonator, these counterpropagating lasers experienced opposing frequency shifts caused by the Sagnac effect [9]. Heterodyne detection of the two laser signals allowed measurement of the rotation rate. As in a conventional ring laser gyro, the counterpropagating laser lines produce a narrow-linewidth beatnote on account of laser action in a high-Q cavity. Co-lasing within a common resonator also tends to cancel technical noise contributions to the beatnote linewidth.In this work, the Brillouin laser cavity is a high-optical-Q micro resonator that measures only 18 mm in diameter and is fabricated of silica on a silicon chip [10]. Also, the method of excitation relies on a single pump wave to induce...