We report on a 10 ksec observation of the double pulsar system J0737–3039 obtained with the Chandra X-ray Observatory ’ s Advanced CCD Imaging Spectrometer . We detect the system as a point source with coordinates ( J2000 ) \mbox { RA } = 07 ^ { h } 37 ^ { m } 51 \fs 23 , \mbox { Decl . } = -30 \arcdeg 39 ^ { \prime } 40 \farcs 9 , making this the first double neutron star system to be detected at X-ray energies . Only 77 source counts are detected . The data are represented satisfactorily by a power-law spectrum with photon index \Gamma = 2.9 \pm 0.4 . The inferred 0.2–10 keV luminosity is \approx 2 \times 10 ^ { 30 } erg s ^ { -1 } for a distance of 0.5 kpc . We do not detect any significant variability with orbital phase in these data , which span one full orbit . These results are consistent with the X-ray emission originating solely from the magnetosphere of the energetic A pulsar , with an efficiency for conversion of rotational energy to X-rays in this band of \sim 0.04 % , although we can not exclude other possibilities .