  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 respectively. 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.
