The response of low energy nuclear recoil in NaI(Tl) is investigated in the following experiment. Such detectors have been used recently to search for evidence of dark matter in the form of weakly interacting massive particles (WIMPs). NaI(Tl) crystal response to nuclear recoil energy deposition is a key element in these searches. I discuss the cosmological and experimental motivations for these experiments, followed by an overview of the physics of direct detection and current relevant WIMP search experiments. With the experiment motivations covered, the details of NaI(Tl) detectors are reviewed. The specifics of our experiment are laid out including the neutron production, neutron beam calibration, shielding optimization, experimental design and setup. Then the crystal response calibration studies and Geant4 simulations are discussed followed by the final quenching factor values and uncertainties. This experiment measured quenching factors for sodium recoils in the energy range of (9 keV-40 keV) of 19%-27% QF. These results are similar to current published measurements. Interesting features of the QF measurements include an increase at low energies and a dip in the values at 30 keV, the iodine K-shell absorption edge. The goal of this experiment was to add valuable measurements of nuclear recoils at low energies that are relevant to low-mass WIMP experiments. Future plans will improve and expand on these measurements in order to better understand the response of NaI(Tl) at low energies.