We report the detection of 8.914 hr variability in both optical and ultraviolet light curves of LP 40-365 (also known as GD 492), the prototype for a class of partly burnt runaway stars that have been ejected from a binary due to a thermonuclear supernova event. We first detected this 1.0% amplitude variation in optical photometry collected by the Transiting Exoplanet Survey Satellite (TESS). Reanalysis of observations from the Hubble Space Telescope at the TESS period and ephemeris reveal a 5.8% variation in the ultraviolet of this 9800 K stellar remnant. We propose that this 8.914 hr photometric variation reveals the current surface rotation rate of LP 40-365, and is caused by some kind of surface inhomogeneity rotating in and out of view, though a lack of observed Zeeman splitting puts an upper limit on the magnetic field of <20 kG. We explore ways in which the present rotation period can constrain progenitor scenarios if angular momentum was mostly conserved, which suggests that the survivor LP 40-365 was not the donor star but was most likely the bound remnant of a mostly disrupted white dwarf that underwent advanced burning from an underluminous (Type Iax) supernova.