The results of the first analysis to show evidence for production of single top quarks are presented. Using 0.9 fb-1 of data collected with the D0 detector at the Fermilab Tevatron, the analysis is performed in the electron jets and muon jets decay modes, taking special care in modeling the large backgrounds, applying a new powerful b-quark tagging algorithm and using three multivariate techniques to extract the small signal in the data. The combined measured production cross section is 4.8 +- 1.3 pb. The probability to measure a cross section at this value or higher in the absence of a signal is 0.027%, corresponding to a 3.5 standard deviation significance.