/ AbstractMeV-GeV dark matter (DM) is theoretically well motivated but remarkably unexplored. This Letter of Intent presents the MeV-GeV DM discovery potential for a 1 m$^3$ segmented plastic scintillator detector placed downstream of the beam-dump at one of the high intensity JLab experimental Halls, receiving up to 10$^{22}$ electrons-on-target (EOT) in a one-year period. This experiment (Beam-Dump eXperiment or BDX) is sensitive to DM-nucleon elastic scattering at the level of a thousand counts per year, with very low threshold recoil energies ($\sim$1 MeV), and limited only by reducible cosmogenic backgrounds. Sensitivity to DM-electron elastic scattering and/or inelastic DM would be below 10 counts per year after requiring all electromagnetic showers in the detector to exceed a few-hundred MeV, which dramatically reduces or altogether eliminates all backgrounds. Detailed Monte Carlo simulations are in progress to finalize the detector design and experimental set up. An existing 0.036 m$^3$ prototype based on the same technology will be used to validate simulations with background rate estimates, driving the necessary R$\&$D towards an optimized detector. The final detector design and experimental set up will be presented in a full proposal to be submitted to the next JLab PAC. A fully realized experiment would be sensitive to large regions of DM parameter space, exceeding the discovery potential of existing and planned experiments by two orders of magnitude in the MeV-GeV DM mass range.