The study is a Phase Ib extension trial that will assess the toxicity, tolerability, and safety of up to two repeated administrations of 1x10^8, 3x10^8, or 1x10^9 autologous Ad-ISF35-transduced CLL B cells given intravenously to patients with CLL who tolerated ISF35 in the prior Phase I infusion trial at M.D. Anderson.