The treatment combination of Rituxan® (rituximab) and fludarabine has previously been reported to produce a high percentage of responses with less toxicity than other combination treatments. However, some leukemia subjects continue to have leukemia despite treatment with these standard anticancer drug therapies, or they may work for only a short period of time. In some subjects, when the leukemia does not respond well to therapy the leukemia cells may be over-producing one or more proteins. One of these proteins is called Bcl-2. Bcl-2 is a protein that appears to protect cancer cells from being killed and thus lengthens the life of the cancer cells. Genasense® (oblimersen sodium) is a compound that blocks production of the Bcl-2 protein. By first lowering levels of Bcl-2, it is possible that chemotherapy drugs may work more effectively as a cancer treatment. Genasense® may also directly kill CLL cells. This study will test whether treating subjects with Genasense®, fludarabine and rituximab is safe and effective.