  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.
