The purpose of this study is to look at the safety and effectiveness of longer term intravenous (IV) infusion of the study drug, nesiritide in patients with acutely decompensated chronic heart failure. Nesiritide (Natrecor) is a man-made version of a human hormone that dilates veins and arteries. Nesiritide (Natrecor) is currently FDA-approved for short-term inpatient IV treatment of acutely decompensated chronic heart failure.