  A massive, but light abelian U(1) gauge boson is a well motivated possible
signature of physics beyond the Standard Model of particle physics. In this
paper, the search for the signal of such a U(1) gauge boson in
electron-positron pair-production at the spectrometer setup of the A1
Collaboration at the Mainz Microtron (MAMI) is described. Exclusion limits in
the mass range of 40 MeV up to 300 MeV with a sensitivity in the mixing
parameter of down to $\epsilon^2 = 8\times 10^{-7}$ are presented. A large
fraction of the parameter space has been excluded where the discrepancy of the
measured anomalous magnetic moment of the muon with theory might be explained
by an additional U(1) gauge boson.
