  Using the full data set of the NA48/2 experiment, the decay K+- -> pi+- e+ e-
gamma is observed for the first time, selecting 120 candidates with 7.3 +- 1.7
estimated background events. With K+- -> pi+- pi0D as normalisation channel,
the branching ratio is determined in a model-independent way to be Br(K+- ->
pi+- e+ e- gamma, m_eegamma > 260 MeV/c^2) = (1.19 +- 0.12_stat +- 0.04_syst) x
10^-8. This measured value and the spectrum of the e+ e- gamma invariant mass
allow a comparison with predictions of Chiral Perturbation Theory.
