We report the first observation of diffractively produced W bosons. In a sample of W -> e nu events produced in ppbar collisions at sqrt s = 1.8 TeV, we find an excess of events with a forward rapidity gap, which is attributed to diffraction. The probability that this excess is consistent with nondiffractive production is 1.1 x 10^-4 (3.8 sigma). The relatively low fraction of W + jet events observed within this excess implies that mainly quarks from the Pomeron, which mediates diffraction, participate in W production. The diffractive to nondiffractive W production ratio is found to be R_W = (1.15 \pm 0.55)%.