We apply a Bayesian method to model multi-epoch radial velocity measurements in the ultra-faint dwarf galaxy Reticulum II , fully accounting for the effects of binary orbital motion and systematic offsets between different spectroscopic datasets . We find that the binary fraction of Ret II is higher than 0.5 at the 90 % confidence level , if the mean orbital period is assumed to be 30 years or longer . Despite this high binary fraction , we infer a best-fit intrinsic dispersion of 2.8 _ { -1.2 } ^ { +0.7 } km/s , which is smaller than previous estimates , but still indicates Ret II is a dark-matter dominated galaxy . We likewise infer a \lesssim 1 % probability that Ret II ’ s dispersion is due to binaries rather than dark matter , corresponding to the regime M _ { \odot / L _ { \odot } } \lesssim 2 . Our inference of a high close binary fraction in Ret II echoes previous results for the Segue 1 ultra-faint dwarf and is consistent with studies of Milky Way halo stars that indicate a high close binary fraction tends to exist in metal-poor environments .