  We present a systematic search for periodic X-ray sources in the bulge of
M31, using ~ 2 Ms of archival Chandra observations spanning a temporal baseline
of 16 years. Utilizing the Gregory-Loredo algorithm that is designed for
photon-counting, phase-folded light curves, we detect seven periodic X-ray
sources, among which four are newly discovered. Three of these sources are
novae, the identified periods of which range between 1.3-2.0 hour and is most
likely the orbital period. The other four sources are low-mass X-ray binaries,
the identified periods of which range between 0.13-19.3 hour and are also
likely orbital due to a clear eclipsing/dipping behavior in the light curve. We
address implications on the X-ray binary population of the M31 bulge. Our study
demonstrates the potential of using archival X-ray observations to
systematically identify periodic X-ray sources in external galaxies, which
would provide valuable information about the underlying exotic stellar
populations.
