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[Abridged] We have carried out a deep X-ray and optical survey with Chandraand HST of low-extinction regions in the Galactic bulge. Here we present theresults of a search for low-luminosity (L_X <~ 1e34 ergs/s) accreting binariesin the region closest to the Galactic Center, at an angular offset of 1.4deg,that we have named the Limiting Window. Based on their blue optical colors,excess Halpha fluxes, and high X-ray--to--optical flux ratios, we identifythree likely cataclysmic variables (CVs). Distance estimates put these systemsfarther than >~2 kpc. Based on their Halpha-excess fluxes and/or highX-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 oractive galaxies. We investigate the CV number density towards the bulge andfind that the number of observed candidate CVs is consistent with or lower thanthe number expected for a constant CV-to-star ratio that is fixed to the localvalue. The X-ray properties of two likely CVs are similar to those of thefaint, hard X-ray sources in the Galactic-Center region that have beenexplained by (mainly) magnetic CVs. If our candidates belong to the samepopulation, they would be the first members to be optically identified; opticalor infrared identification of their Galactic-Center analogs would be impossibledue to the higher obscuration. We speculate that all Galactic hard X-raysources in our field can be explained by magnetic CVs.

ChaMPlane Deep Galactic Bulge Survey. I. Faint accretion-driven binaries in the Limiting Window