  The ACIS instrument on board the Chandra X-ray Observatory has been used to
carry out the first systematic study of low-mass X-ray binaries (LMXBs) in M87.
We identify 174 X-ray point-sources, of which ~150 are likely LMXBs. This LMXB
catalog is combined with deep F475W and F850LP images taken with ACS on HST to
examine the connection between LMXBs and globular clusters in M87. Of the 1688
globular clusters in our catalog, f_X = 3.6 +- 0.5% contain a LMXB and we find
that the metal-rich clusters are 3 +- 1 times more likely to harbor a LMXB than
their metal-poor counterparts. In agreement with previous findings for other
galaxies, we find that brighter, more metal-rich clusters are more likely to
contain a LMXB. For the first time, however, we are able to demonstrate that
the probability, p_X, that a given cluster will contain a LMXB depends
sensitively on the dynamical properties of the host cluster. Specifically, we
use the HST images to measure the half-light radius, concentration index and
central density, \rho_0, for each globular, and define a parameter, \Gamma,
which is related to the tidal capture and binary-neutron star exchange rate.
Our preferred form for p_X is then p_X \propto \Gamma \rho_0^{-0.42\pm0.11}
(Z/Z_{\odot})^{0.33\pm0.1}. We argue that if the form of p_X is determined by
dynamical processes, then the observed metallicity dependence is a consequence
of an increased number of neutron stars per unit mass in metal-rich globular
clusters. Finally, we find no compelling evidence for a break in the luminosity
distribution of resolved X-ray point sources. Instead, the LMXB luminosity
function is well described by a power law with an upper cutoff at L_X ~ 10^39
erg/s. (abridged)
