We report on the first Green Bank Telescope observations at 427 , 820 and 1400 MHz of the newly discovered , highly inclined and relativistic double pulsar binary . We focus on the brief eclipse of PSR J0737 - 3039A , the faster pulsar , when it passes behind PSR J0737 - 3039B . We measure a frequency-averaged eclipse duration of 26.6 \pm 0.6 s , or 0.00301 \pm 0.00008 in orbital phase . The eclipse duration is found to be significantly dependent on radio frequency , with eclipses longer at lower frequencies . Specifically , eclipse duration is well fit by a linear function having slope ( -4.52 \pm 0.03 ) \times 10 ^ { -7 } orbits MHz ^ { -1 } . We also detect significant asymmetry in the eclipse . Eclipse ingress takes 3.51 \pm 0.99 times longer than egress , independent of radio frequency . Additionally , the eclipse lasts ( 40 \pm 7 ) \times 10 ^ { -5 } in orbital phase longer after conjunction , also independent of frequency . We detect significant emission from the pulsar on short time scales during eclipse in some orbits . We discuss these results in the context of a model in which the eclipsing material is a shock-heated plasma layer within the slower PSR J0737 - 3039B ’ s light cylinder , where the relativistic pressure of the faster pulsar ’ s wind confines the magnetosphere of the slower pulsar .