  The chandra monitoring observations of The Antennae (NGC 4038/39) have led to
the discovery of a variable, luminous, supersoft source (SSS). This source is
only detected at energies below 2 keV and, in 2002 May, reached count rates
comparable to those of the nine ultraluminous X-ray sources (ULXs) detected in
these galaxies. Spectral fits of the SSS data give acceptable results only for
a $\sim$100--90 eV blackbody spectrum with an intrinsic absorption column of
$N_{\rm H} \sim 2-3 \times 10^{21} \rm cm^{-2}$. For a distance of 19 Mpc, the
best-fit observed luminosity increases from 1.7$\times 10^{38}$\ergs in 1999
December to 8.0$\times 10^{38}$\ergs in 2002 May. The intrinsic,
absorption-corrected best-fit luminosity reaches 1.4$\times 10^{40}$ \ergs in
2002 May. The assumption of unbeamed emission would suggest a black hole of
$\ga$100\msun. However, if the emission is blackbody at all times, as suggested
by the steep soft spectrum, the radiating area would have to vary by a factor
of $\sim10^3$, inconsistent with gravitational energy release from within a few
Schwarzschild radii of a black hole. Viable explanations for the observed
properties of the SSS are provided by anisotropic emission from either an
accreting nuclear-burning white dwarf or an accreting stellar-mass black hole.
