We report the discovery, by the Chandra X-ray Observatory, of X-ray emission from the bipolar planetary nebula Menzel 3. In Chandra CCD imaging, Mz 3 displays hot (3-6x10^6 K) gas within its twin, coaxial bubbles of optical nebulosity, as well as a compact X-ray source at the position of its central star(s). The brightest diffuse X-ray emission lies along the polar axis of the optical nebula, suggesting a jet-like configuration. The observed combination of an X-ray-emitting point source and possible X-ray jet(s) is consistent with models in which accretion disks and, potentially, magnetic fields shape bipolar planetary nebulae via the generation of fast, collimated outflows.