We present a search for electroweak production of single top quarks in the s-channel and t-channel using neural networks for signal–background separation. We have analyzed 230 pb−1 of data collected with the DØ detector at the Fermilab Tevatron Collider at a center-of-mass energy of 1.96 TeV and find no evidence for a single top quark signal. The resulting 95% confidence level upper limits on the single top quark production cross sections are 6.4 pb in the s-channel and 5.0 pb in the t-channel.