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We report an optical clock recovery system that uses two-photon absorption in a conventional silicon photodiode to synchronize a 10-GHz optical clock to an 80-Gb/s data stream. Compared to many other clock recovery techniques, the system is economical, polarization-insensitive, and can operate over a broad range of optical wavelengths. The system was tested back-to-back and in a 110-km transmission experiment, achieved error-free performance in all cases, and exhibits a root-mean-square timing jitter of 120 fs. Low timing jitter is maintained even in the presence of slow or fast polarization fluctuations.