We report the detection of diffuse hot gas in M31, using archival Chandra observations that allow us to map out a 30' × 30' field (covering a galactocentric radius up to 4.5 kpc) and to detect sources in the galaxy down to a 0.5-8 keV luminosity limit of ~1035 ergs s-1. We estimate the remaining stellar contribution from fainter X-ray sources (primarily cataclysmic variables and coronally active binaries), assuming that they spatially follow the stellar distribution. Indeed, the near-IR K-band light of the galaxy closely traces the 2-8 keV unresolved X-rays, indicating a collective stellar X-ray emissivity consistent with those determined for the Galactic ridge and M32, whereas the amount of the 0.5-2 keV unresolved emission is significantly greater than the expected stellar contribution, especially within a galactocentric radius of ~2 kpc. Morphologically, this soft X-ray excess appears substantially rounder than the bulge as seen in K band and is elongated approximately along the minor-axis at large radii. The excess thus most likely represents the emission of diffuse hot gas in and around the galactic bulge. Furthermore, the near side of the M31 disk casts an apparent shadow against the soft X-ray excess, indicating that the hot gas extends to at least 2.5 kpc from the galactic plane. We briefly discuss the implications of these results on the energy balance in the M31 bulge and on understanding the large-scale soft X-ray enhancement observed toward the inner region of our own Galaxy.