We report on detection of the double pulsar system J0737 - 3039 in the far-UV with the ACS/SBC detector aboard HST . We measured the energy flux F = ( 4.5 \pm 1.0 ) \times 10 ^ { -17 } erg cm ^ { -2 } s ^ { -1 } in the 1250–1550 Å band , which corresponds to the extinction-corrected luminosity L \approx 1.5 \times 10 ^ { 28 } erg s ^ { -1 } for the distance d = 1.1 kpc and a plausible reddening E ( B - V ) = 0.1 . If the detected emission comes from the entire surface of one of the neutron stars with a 13 km radius , the surface blackbody temperature is in the range T \simeq ( 2 – 5 ) \times 10 ^ { 5 } K for a reasonable range of interstellar extinction . Such a temperature requires an internal heating mechanism to operate in old neutron stars , or it might be explained by heating of the surface of the less energetic Pulsar B by the relativistic wind of Pulsar A . If the far-UV emission is non-thermal ( e.g. , produced in the magnetosphere of Pulsar A ) , its spectrum exhibits a break between the UV and X-rays .