 Patients with Congenital Antithrombin Deficiency are at increased risk of venous thrombosis and pulmonary embolism especially when undergoing certain high risk procedures. Antithrombin replacement therapy is often administered during these periods, with or without low molecular weight heparin. Prior to assessing the efficacy of KW-3357, a new recombinant human antithrombin, the present study will determine its pharmacokinetics, safety and tolerability in subjects who have Congenital Antithrombin Deficiency but who are currently asymptomatic and not undergoing a high-risk procedure. Up to 16 evaluable subjects will be enrolled at multiple investigational sites over a period of approximately 7 months. 