RAD001 in Patients With Chronic Phase Chronic Myeloid Leukemia w/ Molecular Disease.

Inclusion Criteria: * Study subjects must be at least age 18 years or older. * Study subjects must have an Eastern Cooperative Oncology Group performance status 0-2. * Study subjects must provide a signed written informed consent. * Study subjects must be able to comply with study procedures and follow-up examinations. * Female study subjects: non-fertile (status post hysterectomy (removal of the uterus) or menopausal (no menstrual period) for 24 consecutive months or agree to use birth control during the study through the end of last treatment visit. Women of childbearing potential must have a negative serum pregnancy test within 3 days prior to administration of RAD001). Use of a single agent for prevention of pregnancy (oral, implantable, or injectable contraceptives) may be affected by medications that alter the activity of the cytochrome P450 enzyme, and are therefore, not considered effective during participation in this clinical trial.If there is ANY chance that pregnant can occur, there must be a commitment to continue abstinence from heterosexual intercourse or begin TWO methods of birth control, one highly effective method and one additional effective method AT THE SAME TIME. * There must be at least two weeks since any major surgery, completion of radiation, or completion of all prior systemic anticancer therapy (adequately recovered from the acute toxicities of any prior therapy). Study subjects must meet the following disease criteria: * Diagnosis of Chronic Myelogenous Leukemia according to the World Health Organization. * Persistent molecular disease as defined by the persistent identification of the Bcr-Abl transcript using quantitative RT-PCR on at least 2 occasions at least 3 months apart and having completed a minimum of 18 months of treatment with Imatinib at 400 mg once daily. * Achieved a complete cytogenetic response. (This shall be measured at least one time prior to consent to participation in the clinical trial, and shall be reassessed at the initiation of the clinical trial.) * Non-hematologic symptoms related to Imatinib therapy that are ≤ Grade 2 in severity for at least 6 months prior to enrollment. Study subjects must meet the following organ function criteria: * Adequate bone marrow function * Adequate renal and hepatic function * International normalized ration \<1.3 (or \<3 on anticoagulants) Study subjects must meet the following cardiac function criteria: * No history of uncontrolled angina, congestive heart failure or myocardial infarction within 6 months of study entry. If there is a suspected clinical history of coronary artery disease, then the patient must document one of the following within 1 year of study participation:Left ventricular ejection fraction greater than 40% on multigated acquisition scan or similar radionuclide angiographic scan; or Left ventricular fractional shortening greater than 22% on echocardiography exam; or LVEF greater than 40% on echocardiography exam. * No history of a diagnosis or suspected congenital QRS complex to the end of the T wave on an electrocardiogram syndrome. * No history of clinically significant ventricular arrhythmias (such as ventricular tachycardia, ventricular fibrillation, or Torsades de pointes). * No history of uncontrolled hypertension. Exclusion Criteria: * Study subjects may not have had prior treatment with RAD001, sirolimus, temsirolimus, or rapamycin. * Study subjects may not have a known hypersensitivity to RAD001 or other rapamycin, sirolimus, temsirolimus or to its excipients. * Study subjects may not have received an investigational agent received within 28 days prior to the first dose of study drug. * Study subjects may not have psychiatric disorders that would interfere with consent, study participation, or follow-up. * Study subjects may not have a history of noncompliance to medical regimens. * Study subjects unwilling to or unable to comply with the protocol are not eligible to participate in this clinical research trial. Study subjects that meet any of the following criteria are not eligible to participate in the clinical research study: * Diagnosis of an accelerated phase or a blast phase of chronic myeloid leukemia according to the World Health Organization criteria. * Clinical evidence suggestive of central nervous system involvement with leukemia unless a lumbar puncture confirms the absence of leukemia in the cerebrospinal fluid. * Prior hematopoietic stem cell transplant. * Prior external beam radiation therapy to the pelvis. * Diagnosis of another malignancy, unless disease-free for at least 3 years following the completion of curative intent therapy with the following exceptions: treatment of non-melanoma skin cancer, in situ carcinoma, or cervical intraepithelial neoplasia, regardless of the disease-free duration - with treatment for the condition complete. * Known chronic condition requiring the treatment with systemic steroids or another immunosuppressive agents. * Systemic fungal, bacterial, viral, or other infection not controlled (defined as exhibiting ongoing signs/symptoms related to the infection and without improvement, despite appropriate antibiotics or other treatment). * Prior seropositive test for the human immunodeficiency virus. * Uncontrolled diabetes mellitus * Impairment of gastrointestinal function or gastrointestinal disease that may significantly alter the absorption of RAD001 (e.g., ulcerative disease, uncontrolled nausea, vomiting, diarrhea, malabsorption syndrome or small bowel resection). * Any other severe concurrent disease, or have a history of serious organ dysfunction or disease involving the heart, kidney, liver, or other organ system that may place the patient at undue risk to undergo therapy with RAD001 including:severely impaired lung function; liver disease such as cirrhosis, chronic active hepatitis or chronic; persistent hepatitis;other nonmalignant medical illnesses that are uncontrolled or whose control may be jeopardized by the treatment with the study therapy. * History of significant bleeding disorder unrelated to cancer, including:Congenital bleeding disorders (e.g., von Willebrand's disease); Acquired bleeding disorder within one year (e.g., acquired anti-factor VIII antibodies).