We report the observation of single top-quark production using 3.2 fb(-1) of pp[over ] collision data with sqrt[s]=1.96 TeV collected by the Collider Detector at Fermilab. The significance of the observed data is 5.0 standard deviations, and the expected sensitivity for standard model production and decay is in excess of 5.9 standard deviations. Assuming m(t) = 175 GeV/c(2), we measure a cross section of 2.3(-0.5);(+0.6)(stat + syst) pb, extract the CKM matrix-element value |V(tb)| = 0.91 + or - 0.11(stat + syst) + or - 0.07(theory), and set the limit |V(tb)| > 0.71 at the 95% C.L.