  We present the results of a 63 ks {\it Chandra} observation of the "supernova
impostor" SN 2010da four months after it was first observed on 25 May 2010. We
detect an X-ray source at $\sim7\sigma$ confidence coincident with the optical
location of the SN 2010da outburst. Our imaging analysis has revealed a hard
central point source, surrounded by soft diffuse emission extending as far as
$\sim$8\asn north of the central source. The diffuse emission has a hardness
ratio, 0.35-2 keV luminosity ($\sim6\times10^{35}$ erg s$^{-1}$), and size
($\sim20$ pc) consistent with that of a supernova remnant, although the low
number of counts prohibits detailed spectral modeling. Our best-fit spectral
model for the hard central source is a black body ($kT = 1.79^{+0.66}_{-0.43}$
keV) with no evidence for intrinsic absorption beyond the Galactic column. We
estimate the 0.3-10 keV luminosity to be 1.7$^{+0.2}_{-0.5}\times10^{37}$ erg
s$^{-1}$, a factor of $\sim$25 decrease since the initial outburst four months
previously. The high X-ray luminosity and slow fading rate is not consistent
with this object being a single massive star undergoing an outburst; instead,
we favor the scenario where the massive star powering the SN 2010da optical
transient is part of a wind-fed supergiant X-ray binary system with a compact
companion powering the observed X-ray emission.
