A new type of fiber interferometer is presented which utilizes a high-finesse all-single-mode-fiber ring resonator. The measured sensitivity to periodic phase shifts induced in the fiber ring is

rad/

or better over the 100-Hz-10-kHz frequency range with maximum sensitivity of

rad/

at 10 kHz. This sensitivity, while high, is not shot-noise limited and appears to be determined by the spectral bandwidth of the single-frequency laser source.