A new exclusion limit for the electromagnetic production of a light U(1) gauge boson γ' decaying to e + e- was determined by the A1 Collaboration at the Mainz Microtron. Such light gauge bosons appear in several extensions of the standard model and are also discussed as candidates for the interaction of dark matter with standard model matter. In electron scattering from a heavy nucleus, the existing limits for a narrow state coupling to e + e- were reduced by nearly an order of magnitude in the range of the lepton pair mass of 210 MeV/c2}<me +}e-<300 MeV/c2. This experiment demonstrates the potential of high current and high resolution fixed target experiments for the search for physics beyond the standard model.