We report a measurement of single top quark production in proton-antiproton collisions at a center-of-mass energy of sqrt[s]=1.96 TeV using a data set corresponding to 7.5 fb(-1) of integrated luminosity collected by the Collider Detector at Fermilab. We select events consistent with the single top quark decay process t→Wb→ℓνb by requiring the presence of an electron or muon, a large imbalance of transverse momentum indicating the presence of a neutrino, and two or three jets including at least one originating from a bottom quark. An artificial neural network is used to discriminate the signal from backgrounds. We measure a single top quark production cross section of 3.04(-0.53)(+0.57) pb and set a lower limit on the magnitude of the coupling between the top quark and bottom quark |Vtb|>0.78 at the 95% credibility level.