About 30% to 50% of the baryons in the local universe are unaccounted for and are likely in a hot phase, to K. A hot halo ( K) is detected around the Milky Way through the O VII and O VIII resonance absorption and emission lines in the soft x-ray band. Current instruments are not sensitive enough to detect this gas in absorption around other galaxies and galaxy groups, the two most likely sites. We show that resonant line absorption by this hot gas can be detected with current technology, with a collecting area exceeding and a spectral resolution . For a few notional x-ray telescope configurations that could be constructed as Explorer or Probe missions, we calculate the differential number of O VII and O VIII absorbers as a function of equivalent width through redshift space, . The hot halos of individual external galaxies produce absorption that should be detectable out to about their virial radii. For the Milky Way, one can determine the radial distribution of density, temperature, and metallicity after making optical depth corrections. Spectroscopic observations can determine the rotation of a hot gaseous halo.