This open-label study will be conducted in up to 20 patients at five clinical sites in the United States. Patients will undergo a 28-day screening period, including a 14-day run-in with AT1001 to assess eligibility for the study. Patients receiving enzyme replacement therapy or substrate depletion therapy for Fabry disease must undergo a 2-week washout of prior therapy before the 28-day screening period. Patients will receive a daily dose of AT1001 for 12 weeks during the treatment phase. The pharmacokinetics of AT1001 in plasma and urine will be assessed at regular intervals. Safety will be evaluated throughout the treatment period. At the end of the 12-week treatment period, the effect of AT1001 on pharmacodynamic parameters (alpha-Gal A in leukocytes, GL-3 in plasma and urine, and alpha-Gal A and GL-3 in skin biopsy samples) and functional parameters (cardiac function as assessed by electrocardiogram, echocardiogram, and MRI, and renal function as assessed by blood and urine tests, and nerve conduction as assessed by QSART and CASE IV tests) will be evaluated. If the safety profile is acceptable, patients will be permitted to enter a 36-week treatment extension period and continue to receive AT1001, with safety, pharmacodynamic, and functional assessments performed at 12-week intervals.