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We study theoretically and demonstrate experimentally generation of coherent optical frequency combs in a sapphire whispering gallery mode resonator. We verify phase locking of the comb harmonics by demodulating the comb on a fast photodiode and by observing the production of a spectrally pure radio frequency signal. Because of excellent optical and superior mechanical properties of the material, the sapphire resonator is an excellent candidate for the on-chip device integration of the comb oscillator. [ABSTRACT FROM AUTHOR]