MeV-GeV dark matter (DM) is theoretically well motivated but remarkably
unexplored. This proposal presents the MeV-GeV DM discovery potential for a
$\sim$1 m$^3$ segmented CsI(Tl) scintillator detector placed downstream of the
Hall A beam-dump at Jefferson Lab, receiving up to 10$^{22}$
electrons-on-target (EOT) in 285 days. This experiment (Beam-Dump eXperiment or
BDX) would be sensitive to elastic DM-electron and to inelastic DM scattering
at the level of 10 counts per year, reaching the limit of the neutrino
irreducible background. The distinct signature of a DM interaction will be an
electromagnetic shower of few hundreds of MeV, together with a reduced activity
in the surrounding active veto counters. A detailed description of the DM
particle $\chi$ production in the dump and subsequent interaction in the
detector has been performed by means of Monte Carlo simulations. Different
approaches have been used to evaluate the expected backgrounds: the cosmogenic
background has been extrapolated from the results obtained with a prototype
detector running at INFN-LNS (Italy), while the beam-related background has
been evaluated by GEANT4 Monte Carlo simulations. The proposed experiment will
be sensitive to large regions of DM parameter space, exceeding the discovery
potential of existing and planned experiments in the MeV-GeV DM mass range by
up to two orders of magnitude.