This letter of intent proposes an experiment to search for an electric dipole moment of the muon based on the frozen-spin technique. We intend to exploit the high electric field, E = 1 GV/m, experienced in the rest frame of the muon with a momentum of p = 125 MeV/c when passing through a large magnetic field of | B| = 3 T. Current muon fluxes at the µE1 beam line permit an improved search with a sensitivity of σ(dµ) ≤ 6 × 10 −23 e•cm, about three orders of magnitude more sensitivity than for the current upper limit of |dµ| ≤ 1.8 × 10 −19 e•cm (C.L. 95%). With the advent of the new high intensity muon beam, HIMB, and the cold muon source, muCool, at PSI the sensitivity of the search could be further improved by tailoring a re-acceleration scheme to match the experiments injection phase space. While a null result would set a significantly improved upper limit on an otherwise un-constrained Wilson coefficient, the discovery of a muon EDM would corroborate the existence of physics beyond the Standard Model.