The progress toward laser cooling an ultracold plasma is presented in this thesis. Ultracold neutral plasmas are created by photo-ionizing laser cooled Strontium atoms. Initially this system is very strongly coupled, however the ions rapidly heat up leaving the plasma on the borderline of the strongly coupled regime. To counteract the effects of this heating an attempt to laser cool the ions in the system is undertaken. However, from these experiments we discovered that velocity changing collisions occurring in the system prevented laser cooling. In order to determine the collisions rate, a collision model was developed to simulate the spectra of the plasma from optical pumping experiments. These experiments and simulations in fact demonstrate that collisions are occurring at a fast enough rate to prevent ion cooling on the time scale of our experiment.