We describe a search for close spectroscopic dwarf M star binaries using data from the Sloan Digital Sky Survey to address the question of the rate of occurrence of multiplicity in M dwarfs. We use a template-fitting technique to measure radial velocities from 145,888 individual spectra obtained for a magnitude-limited sample of 39,543 M dwarfs. Typically, the three or four spectra observed for each star are separated in time by less than four hours, but for ~17% of the stars, the individual observations span more than two days. In these cases we are sensitive to large-amplitude radial velocity variations on timescales comparable to the separation between the observations. We use a control sample of objects having observations taken within a four-hour period to make an empirical estimate of the underlying radial velocity error distribution and simulate our detection efficiency for a wide range of binary star systems. We find the frequency of binaries among the dwarf M stars with a < 0.4 AU to be 3%-4%. Comparison with other samples of binary stars demonstrates that the close binary fraction, like the total binary fraction, is an increasing function of primary mass
