We report on the first deep X-ray survey with the XMM-Newton observatory during the performance verification phase. The field of the Lockman Hole, one of the best studied sky areas over a very wide range of wavelengths, has been observed. A total of ~100 ksec good exposure time has been accumulated. Combining the images of the European Photon Imaging Camera (EPIC) detectors we reach a flux limit of 0.31, 1.4 and 2.4 X 10^{-15} erg cm^{-2} s^{-1}, respectively in the 0.5-2, 2-10, and 5-10 keV band. Within an off-axis angle of 10 arcmin we detect 148, 112 and 61 sources, respectively. The log(N)-log(S) relation in the three bands is compared with previous results. In particular in the 5-10 keV band these observations present the deepest X-ray survey ever, about a factor 20 more sensitive than the previous BeppoSAX observations. Using X-ray spectral diagnostics and the set of previously known, spectroscopically identified ROSAT sources in the field, the new sources can be classified. XMM-Newton detects a significant number (~40%) of X-ray sources with hard, probably intrinsically absorbed X-ray spectra, confirming a prediction of the population synthesis models for the X-ray background.
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