  We report a systematic study of coherent spin precession and spin dephasing
in electron-doped monolayer MoS$_2$. Using time-resolved Kerr rotation
spectroscopy and applied in-plane magnetic fields, a nanosecond-timescale
Larmor spin precession signal commensurate with $g$-factor $|g_0|\simeq 1.86$
is observed in several different MoS$_2$ samples grown by chemical vapor
deposition. The dephasing rate of this oscillatory signal increases linearly
with magnetic field, suggesting that the coherence arises from a sub-ensemble
of localized electron spins having an inhomogeneously-broadened distribution of
$g$-factors, $g_0 + \Delta g$. In contrast to $g_0$, $\Delta g$ is
sample-dependent and ranges from 0.042 to 0.115.
