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Air-core photonic bandgap fibers (PBFs) have great potential for the resonant fiber-optic gyroscope (RFOG), because they reduce both the Kerr-induced drift and the thermal polarization instability. We experimentally studied an open-loop RFOG in which a 20-m resonant loop of 7-cell air-core fiber is closed by connecting the air-core fiber to a conventional single-mode fiber directional coupler. We measured a random walk of 0.055 °/s1/2 and a long-term drift with a standard deviation of 0.5° /s and a peak-to-peak variation of 2.5 °/s over 1 hour. We discuss the sources of error in this RFOG and identify areas for future improvement. We project that with straightforward improvements, tactical-grade performance should be possible.