The guest star of AD 1181 is the only historical supernova of the past millennium that is without a definite counterpart. The previously proposed association with supernova remnant G130.7+3.1 (3C 58) is in strong doubt because of the inferred age of this remnant. Here we report a new identification of SN 1181 with our codiscovery of the hottest known Wolf-Rayet star of the oxygen sequence (IRAS 00500+6713 or 2MASS J00531123+6730023, here named by us as "Parker's star") and its surrounding nebula Pa 30. Our spectroscopy of the nebula shows a fast shock with extreme velocities of approximate to 1100 km s(-1). The derived expansion age of the nebula implies an explosive event approximate to 1000 yr ago that agrees with the 1181 event. The on-sky location also fits the historical Chinese and Japanese reports of SN 1181 to within 3.degrees 5. Pa 30 and Parker's star have previously been proposed to be the result of a double-degenerate merger, leading to a rare Type Iax supernova. The likely historical magnitude and the distance suggest the event was subluminous for normal supernova. This agrees with the proposed Type Iax association that would also be only the second of its kind in the Galaxy. Taken together, the age, location, event magnitude, and duration elevate Pa 30 to prime position as the counterpart of SN 1181. This source is the only Type Iax supernova where detailed studies of the remnant star and nebula are possible. It provides strong observational support for the double-degenerate merger scenario for Type Iax supernovae.