A search for a massless dark photon gamma' is conducted using 4.5 fb(-1) of e(+)e(-) collision data collected at center-of-mass energies between 4.600 and 4.699 GeV with the BESIII detector at ...BEPCII. No significant signal is observed, and the upper limit on the branching fraction B(Lambda(+)(c) -> p gamma') is determined to be 8.0 x 10(-5) at 90% confidence level.