Lymphangioleiomyomatosis (LAM), a disease primarily of women of child-bearing age, is characterized by cystic lung disease and abdominal tumors (e.g., angiomyolipomas). Within the LAM patient population is a subset of patients who develop chylous ascites, chylous pleural effusions, chyluria, peripheral lymphedema, and/or lymphangioleiomyomas. Lymphangioleiomyomas are believed to result from a proliferation of abnormal smooth muscle cells within the lymphatic system, which appears to obstruct fluid outflow, leading to fluid accumulation and an increase in size. The lymphangioleiomyomas may occur anywhere along the axial lymphatic chain. In patients with LAM, they occur most frequently in the thorax, abdomen and pelvis and may give rise to a myriad of symptoms (e.g., paresthesias, palpitations, peripheral edema). In some patients, treatment of many of these symptoms, i.e., elevation of lower extremities, paracentesis, thoracentesis, diuretics, and/or surgery, has been ineffective. Previous studies with somatostatin and octreotide in other clinical settings (e.g., traumatic damage to the lymphatics) have shown a successful reduction in chylous effusions, chyluria, ascites, and peripheral lymphedema, when other therapies were less effective. This study will assess the effectiveness of octreotide in symptomatic patients with LAM, lymphangioleiomyomas and/or chylous effusions/ascites, peripheral lymphedema and chyluria. The dose of octreotide starts at 50 micrograms (ug) by the subcutaneous route twice a day. After two weeks the dose will be increased to 200 ug per day and two weeks later to 400 ug/day. Maximal dose is 400 ug twice a day.