We present first results of a Chandra X-ray observation of the rare oxygen-type Wolf-Rayet (WR) star WR 142 (= Sand 5 = St 3) harbored in the young, heavily obscured cluster Berkeley 87. Oxygen-type WO stars are thought to be the most evolved of the WRs and progenitors of supernovae or gamma-ray bursts. As part of an X-ray survey of supposedly single WR stars, we observed WR 142 and the surrounding Berkeley 87 region with Chandra ACIS-I. We detect WR 142 as a faint yet extremely hard X-ray source. Due to weak emission, its nature as a thermal or non-thermal emitter is unclear and thus we discuss several emission mechanisms. Additionally, we report seven detections and eight non-detections by Chandra of massive OB stars in Berkeley 87, two of which are bright yet soft X-ray sources whose spectra provide a dramatic contrast to the hard emission from WR 142.