  We present a measurement of the fraction of inclusive $W$+jets events
produced with net charm quantum number $\pm1$, denoted $W$+$c$-jet, in
$p\bar{p}$ collisions at $\sqrt{s}=1.96$ TeV using approximately 1~fb$^{-1}$ of
data collected by the D0 detector at the Fermilab Tevatron Collider. We
identify the $W$+jets events via the leptonic $W$ boson decays. Candidate
$W$+$c$-jet events are selected by requiring a jet containing a muon in
association with a reconstructed $W$ boson and exploiting the charge
correlation between this muon and $W$ boson decay lepton to perform a nearly
model-independent background subtraction. We measure the fraction of
$W$+$c$-jet events in the inclusive $W$+jets sample for jet $p_{T}>20$ GeV and
pseudorapidity $|\eta|<2.5$ to be
0.074$\pm0.019$(stat.)$\pm^{0.012}_{0.014}$(syst.), in agreement with
theoretical predictions. The probability that background fluctuations could
produce the observed fraction of $W$+$c$-jet events is estimated to be
$2.5\times 10^{-4}$, which corresponds to a 3.5 $\sigma$ statistical
significance.
