We use high dynamic range, high-resolution L-band spectroscopy to measure the radial velocity variations of the hot Jupiter in the tau Bootis planetary system. The detection of an exoplanet by the shift in the stellar spectrum alone provides a measure of the planets minimum mass, with the true mass degenerate with the unknown orbital inclination. Treating the tau Boo system as a high flux ratio double-lined spectroscopic binary permits the direct measurement of the planets true mass as well as its atmospheric properties. After removing telluric absorption and cross-correlating with a model planetary spectrum dominated by water opacity, we measure a 6-sigma detection of the planet at K_p = 111 +- 5 km/s, with a 1-sigma upper limit on the spectroscopic flux ratio of 10^-4. This radial velocity leads to a planetary orbital inclination of i = 45+3-4degrees and a mass of M_P = 5.90+0.35-0.20 M_ Jup. We report the first detection of water vapor in the atmosphere of a non-transiting hot Jupiter, tau Boo b.