Data from the NA31 experiment at CERN have been used to measure the de
cay K-L --> pi(+/-)e(-/+)v gamma (K-e3 gamma(0)). 1384 +/- 53 events o
f this decay type have been observed, The decay rate relative to K-e3(
0) is found to be Gamma(K-e3 gamma(0), E(gamma) greater than or equal
to 30 MeV, Theta(e-gamma) greater than or equal to 20 degrees)/Gamma
(K-e3(0)) = (0.934 +/- 0.036(stat.)(-0.039)(+0.055)(syst.))% which cor
responds to a branching ratio of BR(K-e3 gamma(0),E(gamma) greater th
an or equal to 30 MeV, Theta(e-gamma) greater than or equal to 20 deg
rees) = (0.361 +/- 0.014(stat.)(-0.015)(+0.021)(syst.))%. The result i
s in good agreement with theoretical predictions, The decay K-L --> pi
(+/-)e(-/+)v gamma is found to be dominated by internal bremsstrahlung
.