The top quark is most often produced in tt pairs via the strong interaction, however, electroweak production of a single top quark is also possible. Electroweak or 'single-top' quark production is more difficult to observe than tt production. A measurement of single-top quark production can provide an interesting test of the Standard Model as well as a measurement of the CKM matrix element Vtb.;This thesis describes a measurement of single-top quark production in pp collisions at s =1.96 TeV using the CDF II detector at the Fermilab Tevatron. This search is performed using a Multivariate Likelihood technique with 2.2 fb-1 of data. The observed cross section for the combined t-channel and s-channel single top cross sections (sigmat and sigmas) is calculated to be sigmas + sigma t = 1.7+0.9-0.8 A measurement of Vtb is derived from this cross section, with the value of |Vtb| = 0.77+0.18-0.21 (exp.) +/- 0.07(theor.), where here the experimental and theoretical errors come from the errors associated with the observed and theoretical single-top cross sections respectively. The probability that this result originates from a background fluctuation, is measured to be 2.40 x 10-2 corresponding to 2.0sigma with an expected probability of 2.32 x 10-4 corresponding to 3.50sigma.