We report the discovery of eight X-ray sources with periodic variability in 487 ks of observations of the Galactic center with Chandra. The sources are identified from a sample of 285 objects detected with 100-4200 net counts. Their periods range from 300 s to 4.5 h with amplitudes between 40% and 70% rms. They have luminosities of (1 - 5) times 10^{32} erg/sec (2--8 keV at 8 kpc). The spectra of seven of the eight sources are consistent with Gamma = 0 power laws absorbed by gas and dust with a column density equal to or higher than that toward the Galactic Center (6 times 10^{22} cm^{-2}). Four of these sources also exhibit emission lines near 6.7 keV from He-like Fe, with equivalent widths of 600-1000 eV. These properties are consistent with both magnetically accreting cataclysmic variables and wind-accreting neutron stars in high-mass X-ray binaries. The eighth source has an absorbing column of 5 times 10^{21} cm^{-2} that places it in the foreground. Its spectrum is consistent with either a Gamma = 1.4 power law or kT = 25 keV bremsstrahlung emission. Its period-folded flux profile clearly identifies it as an eclipsing polar. We place an approximate upper limit of i^prime > 23 magnitude on the optical counterpart to this source using a 5 min exposure obtained with the MagIC camera on the Clay telescope (Magellan II) at Las Campanas.
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