  Recent observations indicate that organic molecules are prevalent towards
starless and prestellar cores. Deuteration of these molecules has not been
well-studied during the starless phase. Published observations of
singly-deuterated methanol, CH$_2$DOH, have only been observed in a couple of
well-studied, dense and evolved prestellar cores (e.g. L1544, L183). Since the
formation of gas-phase methanol during this cold phase is believed to occur via
desorption from the icy grain surfaces, observations of CH$_2$DOH may be useful
as a probe of the deuterium fraction in the ice mantles of dust grains. We
present a systematic survey of CH$_2$DOH towards 12 starless and prestellar
cores in the B10 region of the Taurus Molecular Cloud. Nine of the twelve cores
are detected with [CH$_2$DOH]/[CH$_3$OH] ranging from $< 0.04$ to
$0.23^{+0.12}_{-0.06}$ with a median value of $0.11$. Sources not detected tend
to have larger virial parameters and larger methanol linewidths than detected
sources. The results of this survey indicate that deuterium fractionation of
organic molecules, such as methanol, during the starless phase may be more
easily detectable than previously thought.
