The first observation of the production of a W boson with a single charm quark (c) jet in pp collisions at s√=1.96  TeV is reported. The analysis uses data corresponding to 4.3  fb−1, recorded with the CDF II detector at the Fermilab Tevatron. Charm quark candidates are selected through the identification of an electron or muon from charm-hadron semileptonic decay within a hadronic jet, and a Wc signal is observed with a significance of 5.7 standard deviations. The production cross section σWc(pTc>20  GeV/c,|ηc|<1.5)×B(W→ℓν) is measured to be 13.6+3.4−3.1  pb and is in agreement with theoretical expectations. From this result the magnitude of the quark-mixing matrix element Vcs is derived, |Vcs|=1.08±0.16 along with a lower limit of |Vcs|>0.71 at the 95% confidence level, assuming that the Wc production through c to s quark coupling is dominant.