Stroke is the leading cause of long-term disability in this country with more than 1 million Americans reporting difficulty with daily activities. Loss of independence in self-care tasks is primarily due to limited recovery of the arm. This study will determine if the addition of Transcranial Magnetic Stimulation (TMS) to excite the lesioned hemisphere (side of the brain affected by the stroke), to progressive functional task exercise either of the weakened arm alone or of both arms together will improve arm recovery to a greater degree than one of these two types of arm exercise alone. Individuals post-stroke will participate in 16 sessions of 1) arm rehabilitation alone (with the weaker arm only or with both arms together) or 2) arm rehabilitation plus TMS. The investigators will assess arm movement ability and function immediately following the 4-week intervention and at a 30-day follow-up to determine retention of immediate gains. The investigators hypothesize that those who receive TMS as an adjuvant will have improved arm movement ability than those who only exercise.