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We demonstrate that by driving a fiber optic gyroscope (FOG) with a laser of relatively broad linewidth ( ~ 10 MHz), both the noise and the bias drift are reduced to very low levels (0.058°/√h and 1.1°/h, respectively), comparable to the performance of the same gyroscope conventionally driven with a broadband light source. When the laser linewidth is reduced to a low enough value ( ~ 2.2 kHz), the FOG exhibits a higher drift but an even lower noise, about 4 dB lower than with a broadband source, and only 3.5 dB above shot noise. The measured dependencies of the noise and drift on laser linewidth are in good quantitative agreement with the predictions of an advanced model of backscattering errors in a FOG interrogated with coherent light, which confirms that the noise and drift are predominantly limited by backscattering. The use of a laser comes with the additional benefit of a much greater wavelength stability compared to a broadband source, which is expected to translate directly into a much more stable scale factor than possible in conventional FOGs. Residual sources of drift and the prospects for reducing them in order to achieve inertial navigation performance are discussed.