AT1001-041 is an open-label, non-comparative, multicenter, long term extension study for subjects with Fabry disease who have completed treatment in a previous trial of migalastat HCl (also known as AT1001) given as monotherapy. This is an extension study designed to evaluate the long-term safety and efficacy of migalastat HCl for the treatment of Fabry disease. Study visits will occur every 6 months to evaluate safety and assess efficacy. Visit evaluations will include physical examination, clinical laboratory parameters, adverse events and patient reported outcomes.