• To learn if intensive chemotherapy, with imatinib mesylate (Gleevec, STI571) , followed by maintenance imatinib mesylate plus chemotherapy, followed by imatinib mesylate can improve Philadelphia-positive acute lymphoblastic leukemia. [ Time Frame: 4 Years ] [ Designated as safety issue: No ]
  

• The safety of this treatment will also be studied. [ Time Frame: 4 Years ] [ Designated as safety issue: Yes ]
  

Inclusion:

• Diagnosis of previously untreated Ph-positive ALL or previously treated in CR after 1-2 courses of therapy or failure after one course of induction chemotherapy without imatinib mesylate.
• Age > or = 15 years. Those < 15 years of age will be treated under compassionate IND.
• Zubrod performance status < or = 2 (ECOG Scale, Appendix A).
• Adequate liver function (bilirubin < or = to 3.0 mg/dl, unless considered due to tumor), and renal function (creatinine < or = to 3.0 mg/dl, unless considered due to tumor).
• Adequate cardiac function as assessed clinically by physical examination.
• Signed informed consent.

Exclusion:

• Active serious infection not controlled by oral or intravenous antibiotics.
• Treatment with investigational antileukemic agent or chemotherapy agents in the last 7 days before study entry, unless full recovery from side-effects has occurred or patient has rapidly progressive disease judged life-threatening.
• Active secondary malignancy other than skin cancer (e.g. basal cell carcinoma or squamous cell carcinoma) than in investigator's opinion will shorten survival to less than 1 year.
• History of Grade III/IV cardiac problems as defined by the New York Heart Association Criteria.
• Prior history of treatment with imatinib mesylate.
• Pregnancy or lactating in women of childbearing potential.