DQ Herculis (Nova Herculis 1934) is a deeply eclipsing cataclysmic variable containing a magnetic white dwarf primary. The accretion disk is thought to block our line of sight to the white dwarf at all orbital phases due to its extreme inclination angle. Nevertheless, soft X-rays were detected from DQ Her with ROSAT PSPC. To probe the origin of these soft X-rays, we have performed Chandra ACIS observations. We confirm that DQ Her is an X-ray source. The bulk of the X-rays are from a point-like source and exhibit a shallow partial eclipse. We interpret this as due to scattering of the unseen central X-ray source, probably in an accretion disk wind. At the same time, we observe what appear to be weak extended X-ray features around DQ Her, which we interpret as an X-ray emitting knot in the nova shell.