The primary objective of this study is to determine in patients with traumatic brain injury (TBI) the safe dosing of propranolol. Safety will be measured by episodes of bradycardia (heart rate < 60 beats per minute), hypotension (defined as systolic blood pressure < 90) or decreased cerebral perfusion pressure (defined as CPP less than 60mmHg) that are refractive to Brain Trauma Foundation guidelines for treatment. A no-treatment arm will establish the number of episodes of bradycardia, hypotension and reduced cerebral pressure refractory to treatment that occur without propranolol.