The recent development of low-loss single-mode optical fiber waveguides for light has made possible a new class of inertial reference devices built on the principal of a closed loop interferometer. Light circulating through the loop in both directions experiences a relative phase delay proportional to rotation rate about the loop axis. This paper derives the phase delay and discusses signal detection, signal processing techniques and error sources. It is concluded that synchronous modulation and demodulation and an active gain control at the signal calculation level are required to eliminate drift errors. Potential performance is extraordinarily good; rotation rate sensitivity of a few milli-arc seconds per second and angular position random walk errors of an arc second per square root hour appear feasible.