Monitored drift tube chambers are used as precision tracking detectors in the muon spectrometer of the ATLAS experiment at the LHC at CERN. These chambers provide a spatial resolution of 35 m and a tracking efficiency of close to 100 % up to background rates of 0.5 kHz/cm 2 , the former being limited at higher rates mainly due to space charge effects and the latter due to the maximum drift time of 700 ns. For LHC upgrades, a faster drift tube chamber has been developed, using drift tubes with a diameter of 15 mm instead of 30 mm. The increased channel density and shorter drift time of about 200 ns raise the rate capability to about 10 kHz/cm 2 , while retaining the spatial resolution. A prototype chamber with trapezoidal shape consisting of 2 × 8 layers of 15 mm diameter drift tubes with an active surface of 0.8 m 2 has been constructed. This chamber has been tested at CERN with a 180 GeV muon beam (H8) and with cosmic ray muons at the Gamma Irradiation Facility (GIF) at high radiation rates.