The first measurement of the elementary process mu(-)p --> nu(mu)n gam
ma is reported. A photon pair spectrometer was used to measure the par
tial branching ratio (2.10 +/- 0.22) x 10(-8) for photons of k > 60 Me
V. The value of the weak pseudoscalar coupling constant determined fro
m the partial branching ratio is g(p)(q(2) = -0.88m(mu)(2)) = (9.8 +/-
0.7 +/- 0.3) g(alpha)(0), where the first error is the quadrature sum
of statistical and systematic uncertainties and the second error is d
ue to the uncertainty in lambda(op), the decay rate of the ortho to pa
ra p mu p molecule. This value of g(p) is similar to 1.5 times the pre
diction of partial conservation of axial current and pion-pole dominan
ce.