We describe a nuclear spin gyroscope based on an alkali-metal-noble-gas co-magnetometer. An optically pumped alkali-metal vapor is used to polarize the noble gas atoms and detect their gyroscopic precession. Spin precession due to magnetic fields as well as their gradients and transients can be cancelled in this arrangement. The sensitivity is enhanced by using a high-density alkalimetal vapor in a spin-exchange relaxation free (SERF) regime. With a K-3 He co-magnetometer we demonstrate rotation sensitivity of 5×10 −7 rad/sec/Hz 1/2 . The rotation signal can be increased by a factor of 10 using 21 Ne due to its smaller magnetic moment and the fundamental rotation sensitivity limit for a 21 Ne gyroscope with a 10 cm 3 measurement volume is about 2 × 10 −10 rad/sec/Hz 1/2 .Sensitive gyroscopes find a wide range of applications, from inertial navigation to studies of Earth rotation and tests of general relativity [1]. A variety of physical principles have been utilized for rotation sensing, including mechanical sensing, the Sagnac effect for photons [1,2] and atoms [3,4], the Josephson effect in superfluid 4 He and 3 He [5] and nuclear spin precession [6]. While state-ofthe-art mechanical gyroscopes, such as those developed for Gravity Probe B [7], remain unchallenged in terms of sensitivity, their extremely high cost and difficulty of fabrication motivate the development of simpler, smaller and more robust rotation sensors.Here we describe a new gyroscope based on nuclear spin precession. Unlike the atom and photon interferometric gyroscopes based on the Sagnac effect, nuclear spin gyroscopes do not require a large area enclosed by the interferometer and can be made quite compact. Previous nuclear spin gyroscopes [6] have suffered from high sensitivity to magnetic fields. We show that a comagnetometer using spin-polarized noble gas and alkalimetal vapor can eliminate the sensitivity to magnetic fields, their gradients and transients. High short-term rotation sensitivity can be achieved with an alkali-metal magnetometer operating in the SERF regime [8]. For example, magnetic field sensitivity of 0.5 fT/Hz 1/2 that has been demonstrated in a K magnetometer [9] would result in a rotation sensitivity of 1 × 10 −8 rad/s/Hz 1/2 in a K-21 Ne gyroscope. The bandwidth and transient response of the gyroscope are also significantly improved compared with earlier spin gyroscopes by damping due to coupling between noble gas and alkali-metal spins. We describe an experimental implementation of the gyroscope using K and3 He atoms and demonstrate short term rotation sensitivity of 5 × 10 −7 rad/sec/Hz 1/2 with a sensing volume of only 0.5 cm 3 . We also present a theoretical analysis and experimental measurements of the gyroscope response to various perturbations, and derive fundamental limits for its performance.The co-magnetometer consists of a spherical glass cell containing an alkali metal, several atmospheres of noble gas and a small quantity of nitrogen. Alkali atoms are polarized by optical pumping and transfer the polariz...