  We investigate the prospects for measuring the strange quark distribution
function of the proton in associated $W$ plus charm quark production at the
Tevatron. The $W+c$ quark signal produced by strange quark -- gluon fusion,
$sg\rightarrow W^-c$ and $\bar sg\rightarrow W^+\bar c$, is approximately 5\%
of the inclusive $W+1$ jet cross section for jets with a transverse momentum
$p_T(j)>10$~GeV. We study the sensitivity of the $W$ plus charm quark cross
section to the parametrization of the strange quark distribution function, and
evaluate the various background processes. Strategies to identify charm quarks
in CDF and D\O \ are discussed. For a charm tagging efficiency of about 10\%
and an integrated luminosity of 30~pb$^{-1}$ or more, it should be possible to
constrain the strange quark distribution function from $W+c$ production at the
Tevatron.
