The D0 Collaboration presents first evidence for the production of single top quarks at the Fermilab Tevatron < p(p)over bar > collider. Using a 0.9 fb(-1) dataset, we apply a multivariate analysis to separate signal from background and measure sigma(< p(p)over bar >-> tb+X,tqb+X)=4.9 +/- 1.4 pb. The probability to measure a cross section at this value or higher in the absence of a signal is 0.035%, corresponding to a 3.4 standard deviation significance. We use the cross section measurement to directly determine the Cabibbo-Kobayashi-Maskawa matrix element that describes the Wtb coupling and find 0.68 <vertical bar V-tb vertical bar <= 1 at 95% C.L. within the standard model.