A total of 375 new radial velocities have been obtained for the 111 giants in the globular cluster M3, previously observed by Gunn and Griffin (1979). The velocities have a typical accuracy of 0.9 km/s per measurement and have been combined with the Gunn and Griffin data in order to search for radial-velocity variations over a timespan of more than 10 years. One star, von Zeipel 164, shows strong evidence for being a spectroscopic binary. Modeling of the velocity variations that would be expected for a variety of binary populations confirms Gunn and Griffin's conclusion that binaries with separations less than 10 AU must occur less frequently among the giants of M3 than among the population I field stars. However, it is argued that it is premature to conclude that M3 formed with a deficiency of binaries, and mechanisms that may have removed primordial binaries from the present sample of giants are discussed.