We describe a search for production of a charged Higgs boson, q¯q′→H+, reconstructed in the t¯b final state in the mass range 180≤MH+≤300 GeV. The search was undertaken at the Fermilab Tevatron collider with a center-of-mass energy √s=1.96 TeV and uses 0.9 fb−1 of data collected with the D0 detector. We find no evidence for charged Higgs boson production and set upper limits on the production cross section in the types I, II, and III two-Higgs-doublet models (2HDMs). An excluded region in the (MH+, tanβ) plane for type I 2HDM is presented.Received 8 July 2008DOI:https://doi.org/10.1103/PhysRevLett.102.191802©2009 American Physical Society