An observational test of the binary hypothesis for the origin of blue straggler stars is conducted by searching for radial velocity variables among 30 blue stragglers in several galactic clusters. Only one of the slowly rotating blue stragglers is detected as a radial velocity variable, and it is shown that this finding does not correspond to the close binary model at the 99 percent confidence level. It is concluded that binarity is almost certainly not a causal requirement for any blue straggler. The results are compared to the binary distribution expected under the model of Collier and Jenkins (1984).