We are writing this letter to express our interest in pursuing an experiment at Fermilab to search for neutrinoless conversion of muons into electrons in the field of a nucleus, which is a lepton flavor-violating (LFV) reaction. The sensitivity goal of this experiment represents an improvement of more than a factor of 10,000 over existing limits. It would provide the most sensitive test of LFV, a unique and essential window on new physics unavailable at the high energy frontier. We present a

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... ceptual scheme that would exploit the existing Fermilab Accumulator and Debuncher rings to generate the required characteristics of the primary proton beam. The proposal requires only modest modifications to the accelerator complex beyond those already planned for the NOvA experiment, with which this experiment would be fully compatible; however, it could also benefit significantly from possible upgrades such as the "Project X" linac. We include the conceptual design of the muon beam and the experimental apparatus, which use the previously proposed MECO experiment as a starting point.