The Ricochet experiment seeks to measure Coherent (neutral-current) Elastic Neutrino-Nucleus Scattering using dark-matter-style detectors with sub-keV thresholds placed near a neutrino source, such as the MIT (research) Reactor (MITR), which operates at 5.5 MW generating approximately 2.2e18 neutrinos/second in its core. Currently, Ricochet is characterizing the backgrounds at MITR, the main component of which comes in the form of neutrons emitted from the core simultaneous with the neutrino signal. To characterize this background, we wrapped Bonner cylinders around a He-3 thermal neutron detector, whose data was then unfolded via a Markov Chain Monte Carlo (MCMC) to produce a neutron energy spectrum across several orders of magnitude. We discuss the resulting spectrum and its implications for deploying Ricochet at the MITR site as well as the feasibility of reducing this background level via the addition of polyethylene shielding around the detector setup.