A Short-Baseline Neutrino (SBN) physics program of three LAr-TPC detectors located along the Booster Neutrino Beam (BNB) at Fermilab is presented. This new SBN Program will deliver a rich and compelling physics opportunity, including the ability to resolve a class of experimental anomalies in neutrino physics and to perform the most sensitive search to date for sterile neutrinos at the eV mass-scale through both appearance and disappearance oscillation channels. Using data sets of 6.6e20 protons on target (P.O.T.) in the LAr1-ND and ICARUS T600 detectors plus 13.2e20 P.O.T. in the MicroBooNE detector, we estimate that a search for muon neutrino to electron neutrino appearance can be performed with ~5 sigma sensitivity for the LSND allowed (99% C.L.) parameter region. In this proposal for the SBN Program, we describe the physics analysis, the conceptual design of the LAr1-ND detector, the design and refurbishment of the T600 detector, the necessary infrastructure required to execute the program, and a possible reconfiguration of the BNB target and horn system to improve its performance for oscillation searches.