This study will find out whether electrical stimulation of a nerve called the "vagus" nerve is acceptable for patients undergoing physiotherapy for arm weakness after a stroke. 20 patients will be recruited if they had a stroke between 4 and 48 months previously and have been left with reduced function in the affected arm. Patients will receive 3 sessions of physiotherapy per week for 6 weeks. Each session will last 1 hour during which the patient will be asked to perform specific movements e.g. shuffling cards, reaching for a shelf. With each arm movement the therapist will turn on a stimulator which is worn clipped to the patients ear. This will deliver a short burst of electricity creating a mild tingling sensation.