Studies of the performance of the CMS drift tube barrel muon system are described, with results based on data collected during the CMS Cosmic Run at Four Tesla. For most of these data, the solenoidal magnet was operated with a central field of 3.8 T. The analysis of data from 246 out of a total of 250 chambers indicates a very good muon reconstruction capability, with a coordinate resolution for a single hit of about 260 μm, and a nearly 100% efficiency for the drift tube cells. The resolution of the track direction measured in the bending plane is about 1.8 mrad, and the efficiency to reconstruct a segment in a single chamber is higher than 99%. The CMS simulation of cosmic rays reproduces well the performance of the barrel muon detector.