This is a study of infusional doxorubicin, vincristine, and etoposide in combination with daily oral mitotane in patients with adrenocortical cancer. Although mitotane has been used extensively in adrenocortical cancer and has documented single agent activity, only limited experience is available in the use of mitotane in combination with chemotherapy. In this trial the primary reason for using mitotane is an attempt to enhance therapeutic efficacy, based on its documented in-vitro activity as an antagonist of P-glycoprotein. The goal of this study is to determine the efficacy of this therapy by treating patients who are considered candidates for surgical resection at presentation or following a response to therapy. Following chemotherapy, patients deemed surgical candidates can undergo surgical resection with evaluation of response. Patients responding to chemotherapy will resume the combination treatment after surgery. Patients who do not respond will be maintained on single agent mitotane until it is deemed ineffective.