We have carried out a deep X-ray and optical survey with Chandra and HST of low-extinction regions in the Galactic bulge. Here we present the results of a search for low-luminosity (L_X_<~10^34^erg/s) accreting binaries among the Chandra sources in the region closest to the Galactic center, at an angular offset of 1.4{deg}, that we have named the Limiting Window (LW). Based on their blue optical colors, excess H{alpha} fluxes, and high X-ray-to-optical flux ratios, we identify three likely accreting binaries; these are probably white dwarfs accreting from low-mass companions (cataclysmic variables; CVs) although we cannot exclude that they are quiescent neutron-star or black-hole low-mass X-ray binaries. Distance estimates put these systems farther than >~2kpc. Based on their H{alpha}-excess fluxes and/or high X-ray-to-optical flux ratios, we find 22 candidate accreting binaries; however, the properties of some can also be explained if they are dMe stars or active galaxies.