We present a search for electroweak production of single top quarks in the s-channel (p[overline p]-->t[overline b]+X) and t-channel (p[overline p]-->tq[overline b]+X) modes. We have analyzed 230 pb-1 of data collected with the D0 detector at the Fermilab Tevatron Collider at a center-of-mass energy of sqrt(s)=1.96 TeV. No evidence for a single top quark signal is found. We set 95% confidence level upper limits on the production cross sections, based on binned likelihoods formed from a neural network output. The observed (expected) limits are 6.4 pb (4.5 pb) in the s-channel and 5.0 pb (5.8 pb) in the t-channel.