We report first results from the ZEPLIN I dark matter detector, based on measurement of scintillation pulse shapes in a liquid xenon target of 3.2 kg fiducial mass. Neutron calibration shows nuclear recoil pulses to have a time constant ≅ 0.5 that of gamma and beta background events. The detector is located in the 2800 mwe depth UK Boulby Mine, and is surrounded by a liquid scintillator Compton veto and passive lead shielding. Three runs totaling 293 kg d fiducial exposure yielded data consistent with a single population of background pulses, with no significant low energy population of shorter pulses. From the 90% confidence limit on the latter a limit is derived on the spin-independent WIMP-nucleon cross-section versus particle mass with a minimum at 1.1 × 10−6 pb.