  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, $E=1{\rm GV/m}$, experienced in the rest frame of the muon
with a momentum of $p=125 {\rm MeV/}c$ when passing through a large magnetic
field of $|\vec{B}|=3{\rm T}$. Current muon fluxes at the $\mu$E1 beam line
permit an improved search with a sensitivity of $\sigma(d_\mu)\leq
6\times10^{-23}e{\rm cm}$, about three orders of magnitude more sensitivity
than for the current upper limit of $|d_\mu|\leq1.8\times10^{-19}e{\rm
cm}$\,(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.
