The resolution and efficiency of a precision drift-tube chamber for the ATLAS muon spectrometer with final read-out electronics was tested at the Gamma Irradiation Facility at CERN in a 100 GeV muon beam and at photon irradiation rates of up to 990 Hz/square cm which corresponds to twice the highest background rate expected in ATLAS. A silicon strip detector telescope was used as external reference in the beam. The pulse-height measurement of the read-out electronics was used to perform time-slewing corrections which lead to an improvement of the average drift-tube resolution from 104 microns to 82 microns without irradiation and from 128 microns to 108 microns at the maximum expected rate. The measured drift-tube efficiency agrees with the expectation from the dead time of the read-out electronics up to the maximum expected rate.
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