Inclusion Criteria:

- Histologically confirmed chronic myelogenous leukemia (CML)

- Philadelphia chromosome-positive OR Bcr-Abl-positive disease, meeting 1 of the
following criteria:

- Accelerated phase, defined by at least 1 of the following:

- 10-19% blasts in the peripheral blood or bone marrow

- At least 20% basophils in peripheral blood or bone marrow

- Platelet count < 100,000/mm^3 (unrelated to therapy)

- Platelet count > 1,000,000/mm^3 (unresponsive to therapy)

- Increasing splenomegaly AND increasing WBC count (unresponsive to
therapy)

- Clonal evolution

- Blast phase, defined by 1 of the following:

- At least 20% blasts in peripheral blood or bone marrow

- Extramedullary disease

- Chronic phase, defined by all of the following:

- Less than 10% blasts in peripheral blood or bone marrow

- Less than 20% basophils in peripheral blood or bone marrow

- Platelet count > 100,000/mm^3

- Absence of clonal evolution

- May have received and/or failed prior imatinib mesylate therapy

- Patients not previously treated with imatinib mesylate receive oral imatinib
mesylate once daily 14 days before beginning study drug

- Must be able to tolerate 600 mg per day of imatinib mesylate before
starting CCI-779

- Patients with chronic phase disease must have failed prior imatinib mesylate at
a dose ≥ 600 mg/day, as defined by 1 of the following:

- Must not have achieved or must have lost hematologic response within 3
months after the start of imatinib mesylate

- Must not have achieved or must have lost cytogenetic response after 6
months of treatment with imatinib mesylate

- Must not have achieved or must have lost major cytogenetic response after
12 months of treatment with imatinib mesylate

- Must have lost complete cytogenetic response

- Bone marrow aspirate and biopsy with cytogenetics and fluorescent in situ
hybridization confirming t(9;22) completed within the past 28 days

- Performance status - SWOG 0-2

- More than 3 months

- See Disease Characteristics

- Bilirubin normal

- AST and ALT < 2.5 times upper limit of normal (ULN) (5 times ULN if suspected liver
involvement with leukemia)

- Creatinine normal

- Creatinine clearance > 60 mL/min

- No symptomatic congestive heart failure

- No unstable angina pectoris

- No cardiac arrhythmia

- Ejection fraction ≥ 50% by echocardiogram or MUGA scan for patients with known
positive cardiac history (e.g., heart failure, coronary artery disease, cardiomegaly
on prior chest x-ray, or valvular heart disease)

- Not pregnant or nursing

- Negative pregnancy test

- Fertile patients must use effective contraception

- Fasting cholesterol ≤ 350 mg/dL

- Fasting triglycerides ≤ 400 mg/dL

- No history of allergic reaction attributed to compounds of similar chemical or
biologic composition to temsirolimus or imatinib mesylate

- No active or ongoing infection

- No psychiatric illness or social situation that would preclude study compliance

- No other active malignancy except nonmelanoma skin cancer

- No other uncontrolled illness

- At least 48 hours since prior interferon alfa for CML

- At least 6 weeks since prior stem cell transplantation

- No concurrent biologic agents

- No concurrent prophylactic colony-stimulating factors

- At least 24 hours since prior hydroxyurea for CML

- At least 7 days since prior mercaptopurine or vinca alkaloids for CML

- At least 7 days since prior low-dose cytarabine (< 30 mg/m^2 every 12-24 hours) for
CML

- At least 14 days since prior homoharringtonine for CML

- At least 14 days since prior moderate-dose cytarabine (100-200 mg/m^2 for 5-7 days)
for CML

- At least 21 days since prior anthracyclines, mitoxantrone, cyclophosphamide,
etoposide, or methotrexate for CML

- At least 28 days since prior high-dose cytarabine (1-3 g/m^2 every 12-24 hours for
6-12 doses) for CML

- At least 6 weeks since prior busulfan for CML

- No concurrent hydroxyurea

- No other concurrent chemotherapy

- At least 7 days since prior steroids for CML

- No prior organ transplantation

- More than 2 weeks since prior major surgery (e.g., thoracotomy or intra-abdominal
surgery)

- Recovered from all prior therapy

- Prior experimental therapy allowed provided completion of treatment corresponds to a
duration > 5 half-lives of the experimental drug or any known active metabolite
before study

- No concurrent cyclosporine

- No concurrent anagrelide

- No concurrent oral anticoagulants, including warfarin

- No concurrent CYP3A4 inducers or inhibitors

- No concurrent tacrolimus

- No concurrent plasmapheresis

- No concurrent combination antiretroviral therapy for HIV-positive patients

- No other concurrent investigational agents

- No other concurrent anticancer therapies