We report the discovery of an optical counterpart to a quiescent neutron star in the globular cluster Omega Centauri (NGC 5139). The star was found as part of our wide-field imaging study of Omega Cen using the Advanced Camera for Surveys (ACS) on Hubble Space Telescope. Its magnitude and color (R_625 = 25.2, B_435 - R_625 = 1.5) place it more than 1.5 magnitudes to the blue side of the main sequence. Through an H-alpha filter it is ~ 1.3 magnitudes brighter than cluster stars of comparable M_625 magnitude. The blue color and H-alpha excess suggest the presence of an accretion disk, implying that the neutron star is accreting from a binary companion and is thus a quiescent low-mass X-ray binary. If the companion is a main-sequence star, then the faint absolute magnitude (M_625 ~ 11.6) constrains it to be of very low mass (M <~ 0.14 Msolar). The faintness of the disk (M_435 ~ 13) suggests a very low rate of accretion onto the neutron star. We also detect 13 probable white dwarfs and three possible BY Draconis stars in the 20 x 20 region analyzed here, suggesting that a large number of white dwarfs and active binaries will be observable in the full ACS study.