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 \times 10 ^ { 9 } M _ { \odot } . When this profile is extrapolated to 500 kpc ( the approximate virial radius ) , the implied hot halo mass is 1 - 3 \times 10 ^ { 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 .