  We report the first measurement of a structure dependent component in the
decay K^+ -> mu^+ nu gamma. Using the kinematic region where the muon kinetic
energy is greater than 137 MeV and the photon energy is greater than 90 MeV, we
find that the absolute value of the sum of the vector and axial-vector form
factors is |F_V+F_A| =0.165 \pm 0.007 \pm 0.011. This corresponds to a
branching ratio of BR(SD^+) = (1.33 \pm 0.12 \pm 0.18) \times 10^{-5}. We also
set the limit -0.04 < F_V-F_A < 0.24 at 90% c.l.
