We report on the measurement at 820- and 1400-MHz of orbital modulation of the diffractive scintillation timescale from pulsar A in the double-pulsar system J0737-3039 using the Green Bank Telescope. Fits to this modulation determine the systemic velocity in the plane of the sky to be V_iss ~ 140.9 +/- 6.2 km/s. The parallel and perpendicular components of this velocity with respect to the line of nodes of the pulsar's orbit are V_plane ~ 96.0 +/- 3.7 km/s and V_perp ~ 103.1 +/- 7.7 km/s

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... ively. The large V_perp implies that pulsar B was born with a kick speed of >~ 100 km/s. Future VLBA determination of the angular proper motion in conjunction with improved V_iss measurements should provide a precise distance to the system. Using high-precision timing data and the V_iss model, we estimate a best-fit orbital inclination of i = 88.7 +/- 0.9 deg.