We introduce the Galactic Bulge Survey (GBS) and we provide the Chandra source list for the region that has been observed to date. Among the goals of the GBS are constraining the neutron star equation of state and the black hole mass distribution via the identification of eclipsing neutron star and black hole low-mass X-ray binaries. The latter goal will, in addition, be obtained by significantly enlarging the number of black hole systems for which a black hole mass can be derived. Further goals include constraining X-ray binary formation scenarios, in particular the common envelope phase and the occurrence of kicks, via source-type number counts and an investigation of the spatial distribution of X-ray binaries, respectively. The GBS targets two strips of 6x1 degrees (12 square degrees in total), one above (1<b<2 degrees) and one below (-2<b<-1 degrees) the Galactic plane in the direction of the Galactic Center at both X-ray and optical wavelengths. By avoiding the Galactic plane (-1<b<1 degrees) we limit the influence of extinction on the X-ray and optical emission but still sample relatively large number densities of sources. The survey is designed such that a large fraction of the X-ray sources can be identified from their optical spectra. The X-ray survey, by design, covers a large area on the sky while the depth is shallow using 2 ks per Chandra pointing. In this way we maximize the predicted number ratio of (quiescent) low-mass X-ray binaries to Cataclysmic Variables. The survey is approximately homogeneous in depth to an 0.5-10 keV flux of 7.7x10^-14 erg cm-2 s-1. So far, we have covered about two-thirds (8.3 square degrees) of the projected survey area with Chandra providing over 1200 unique X-ray sources. We discuss the characteristics and the variability of the brightest of these sources.