This invention is directed to a system and method for partitioning a patient's heart chamber into a productive portion and a non-productive portion which are particularly suitable for treating patients with congestive heart failure. The partitioning system has a plurality of partitioning devices with reinforced, expandable membranes which separate the productive and non-productive portions of the heart chamber. When deployed within the patient's heart chamber, the second partitioning device is off-set from the deployed first partitioning device to cover a region of the wall defining the patient's heart chamber which is not covered by the first partitioning device. The multiple partitioning devices may be independent from each other or may be interconnected, e.g. a tether or strand.