Although the fiber optic gyroscope (FOG) continues to be a commercial success, current research efforts are endeavoring to improve its precision and broaden its applicability to other markets, in particular the inertial navigation of aircraft. Significant steps in this direction are expected from the use of (1) laser light to interrogate the FOG instead of broadband light, and (2) a hollow-core fiber (HCF) in the sensing coil instead of a conventional solid-core fiber. The use of a laser greatly improves the FOG’s scale-factor stability and eliminates the source excess noise, while an HCF virtually eliminates the Kerr-induced drift and significantly reduces the thermal and Faraday-induced drifts. In this paper we present theoretical evidence that in a FOG with a 1085-m coil interrogated with a laser, the two main sources of noise and drift resulting from the use of coherent light can be reduced below the aircraft-navigation requirement by using a laser with a very broad linewidth, in excess of 40 GHz. We validate this concept with a laser broadened with an external phase modulator driven with a pseudo-random bit sequence at 2.8 GHz. This FOG has a measured noise of 0.00073 deg/√h, which is 30% below the aircraft-navigation requirement. Its measured drift is 0.03 deg/h, the lowest reported for a laser-driven FOG and only a factor of 3 larger than the navigation-grade specification. To illustrate the potential benefits of a hollow-core fiber in the FOG, this review also summarizes the previously reported performance of an experimental FOG utilizing 235 m of HCF and interrogated with broadband light.