We obtained an optical spectrum of a star we identify as the optical counterpart of the M31 Chandra source CXO J004318.8+412016, because of prominent emission lines of the Balmer series, of neutral helium, and a He II line at 4686 Angstrom. The continuum energy distribution and the spectral characteristics demonstrate the presence of a red giant of K or earlier spectral type, so we concluded that the binary is likely to be a symbiotic system. CXO J004318.8+412016 has been observed in X-rays as a luminous supersoft source (SSS) since 1979, with effective temperature exceeding 40 eV and variable X-ray luminosity, oscillating between a few times 10(35) erg/s and a few times 10(37) erg/s. The optical, infrared and ultraviolet colors of the optical object are consistent with an an accretion disk around a compact object companion, which may either be a white dwarf, or a black hole, depending on the system parameters. If the origin of the luminous supersoft X-rays is the atmosphere of a white dwarf that is burning hydrogen in shell, it is as hot and luminous as post-thermonuclear flash novae, yet no major optical outburst has ever been observed, suggesting that the white dwarf is very massive (m>1.2 M(sol)) and it is accreting and burning at the high rate (mdot>10(-8)M(sol)/year) expected for type Ia supernovae progenitors. In this case, the X-ray variability may be due to a very short recurrence time of only mildly degenerate thermonuclear flashes.
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