Inclusion Criteria:

1. Female, age 18 or over
2. Signed and dated informed consent
3. Diagnosis of LAM as determined by compatible lung CT and one of the following

1. biopsy (lung, abdominal mass, lymph node or kidney) or cytology from thoracic or abdominal sources revealing LAM, or
2. tuberous sclerosis, angiomyolipomata (diagnosed by CT, MRI by the site radiologist or biopsy) or chylous pleural effusion (verified by tap), or
3. VEGF-D level ≥ 800 pg/ml.
4. Post-bronchodilator forced expiratory volume in one second of \> 70%
5. Presence of markers of non-trivial burden of LAM or likely progression based on one of the following:

1. pretrial FEV 1 rate of decline of \>60cc/yr, comparing enrollment FEV1 to any prior measurement in the past 3 years, or
2. baseline supplemental oxygen requirement with exercise, or
3. pre-menopausal and one of the following (if post-menopausal, must have a VEGF-D level ≥ 600 pg/ml and one of the following) baseline diffusing capacity for carbon monoxide ≤80% predicted,

a) baseline residual volume ≥120% predicted, b) baseline desaturation by 4% or more on six minute walk testing on room air c) more than 20 cysts on the carinal cut of the CT

Exclusion Criteria:

1. Existing or imminent (within 12-18 months) clinical indication for treatment with mTOR inhibitors, based on judgment of site investigator
2. DLCO \<60% predicted
3. Resting room air saturation \<90%
4. Exercise induced desaturation nadir on room air \< 85%
5. History of myocardial infarction, angina or stroke related to atherosclerosis
6. Pregnant, breast feeding, or plan to become pregnant in the next 2.5 years
7. Inadequate contraception
8. Significant hematologic, renal, metabolic or hepatic abnormality (i.e. transaminase levels \> three times the UL of normal range, HCT \< 30%, platelets \< 80,000/mm3, adjusted absolute neutrophil count \< 1,000/ mm3, total WBC \< 3,000/ mm3), creatinine \>2.5 mg/dl, uncontrolled hyperlipidemia
9. Acute or chronic infection, such as (nontuberculous mucobacteria or active hepatitis B or C infections)
10. Recent surgery (involving entry into a body cavity or requiring 3 or more sutures) within three weeks of initiation of study drug
11. Use of sirolimus, everolimus or investigational treatment for LAM within the 30 days prior to randomization
12. Previous lung transplantation or active on transplant list
13. Inability to attend scheduled clinic visits, or perform pulmonary function testing
14. Pleural effusion or chylous ascites sufficient to affect pulmonary function based on the opinion of the Site Investigator
15. Acute pneumothorax within the past month
16. History of malignancy in the past two years, other than squamous or basal cell skin cancer.
17. Use of estrogen containing medications within the 30 days prior to randomization.
18. Known allergy to sirolimus