  We present a systematic study of periodic X-ray sources in the Limiting
Window (LW), a $\sim$70 arcmin$^2$ field representative of the inner Galactic
bulge and the target of $\sim$1 Ms Chandra observations. Using the
Gregory-Loredo algorithm, which applies Bayes's theorem to the phase-folded
light curve and is well-suited for irregularly sampled X-ray data, we detect 25
periodic signals in 23 discrete sources, among which 15 signals are new
discoveries and two sources show dual periods. The vast majority of the 23
periodic sources are classified as magnetic cataclysmic variables (CVs), based
on their period range, X-ray luminosities, spectral properties, and
phase-folded light curves that are characteristic of spin modulation.
Meanwhile, there is a paucity of non-magnetic CVs seen as periodic sources,
which can be understood as due to a low detection efficiency for eclipsing
sources. Under reasonable assumptions about the geometry of magnetic CVs and a
large set of simulated X-ray light curves, we estimate the fraction of magnetic
CVs in the inner Galactic bulge to be $\lesssim$23%, which is similar to that
in the solar neighborhood. There is an apparent lack of long-period
($\gtrsim$3.3 hours) CVs in the LW, when contrasted with the range of known CVs
in the solar neighborhood. We suggest that this might be an age effect, in the
sense that CVs in the inner bulge are more evolved systems and have
substantially shrunk their orbits.
