The purpose of this double-blind, placebo-controlled, dose-response study is to evaluate the safety, tolerability and effectiveness of Thymosin Beta 4 (Tβ4), administered topically, in patients with Venous Stasis (VS) ulcers. VS ulcers develop on the ankle or lower leg in patients with chronic vascular disease. In these patients, blood flow in the lower extremities is impaired, leading to edema (swelling) and mild redness and scaling of the skin that gradually progress to ulceration. Tβ4 is a synthetically-produced copy of a naturally occurring 43 amino acid peptide that has wound healing and anti-inflammatory properties and can up-regulate the expression of laminin-5.