We report the first observation of the Dalitz decay eta' -> gamma e(+)e(-), based on a data sample of 1.31 billion J/psi events collected with the BESIII detector. The eta' mesons are produced via the J/psi -> gamma eta' decay process. The ratio (eta' -> gamma e(+)e(-))/Gamma (eta' -> gamma gamma) is measured to be (2.13 +/- 0.09(stat) +/- 0.07(sys)) x 10(-2). This corresponds to a branching fraction B(eta' -> gamma e(+)e(-)) = (4.69 +/- 0.20(stat) +/- 0.23(sys)) x 10(-4). The transition form factor is extracted and different expressions are compared to the measured dependence on the e(+)e(-) invariant mass. The results are consistent with the prediction of the vector meson dominance model.