  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.
