  Hot gaseous halos are predicted around all large galaxies and are critically
important for our understanding of galaxy formation, but they have never been
detected at distances beyond a few kpc around a spiral galaxy. We used the
Chandra ACIS-I instrument to search for diffuse X-ray emission around an ideal
candidate galaxy: the isolated giant spiral NGC 1961. We observed four
quadrants around the galaxy for 30 ks each, carefully subtracting background
and point source emission, and found diffuse emission that appears to extend to
40-50 kpc. We fit $\beta$-models to the emission, and estimate a hot halo mass
within 50 kpc of $5\times10^9 M_{\odot}$. When this profile is extrapolated to
500 kpc (the approximate virial radius), the implied hot halo mass is
$1-3\times10^{11} M_{\odot}$. These mass estimates assume a gas metallicity of
$Z = 0.5 Z_{\odot}$. This galaxy's hot halo is a large reservoir of gas, but
falls significantly below observational upper limits set by pervious searches,
and suggests that NGC 1961 is missing 75% of its baryons relative to the cosmic
mean, which would tentatively place it below an extrapolation of the baryon
Tully-Fisher relationship of less massive galaxies. The cooling rate of the gas
is no more than 0.4 $M_{\odot}$/year, more than an order of magnitude below the
gas consumption rate through star formation. We discuss the implications of
this halo for galaxy formation models.
