This study involves being treated initially with a combination of drugs called irinotecan and cisplatin (induction therapy), followed by treatment with a drug called Gleevec (maintenance therapy). The main purpose of this study is to determine if this type of treatment will delay the growth of the tumor and if so, for how long. The investigators also want to find out how the tumor is affected solely by induction therapy with irinotecan and cisplatin, what side-effects occur when Gleevec maintenance therapy is used, and if this treatment (induction followed by maintenance therapy) will improve the duration of survival

Inclusion Criteria:

1. Histologically or cytologically confirmed extensive-stage SCLC, which is c-kit-positive by immunohistochemistry. Extensive-stage is defined as disease that extends beyond one hemithorax and regional lymph nodes (ipsilateral or contralateral hilar, mediastinal or supraclavicular lymph nodes), or with cytologically positive pleural effusion.
2. No prior chemotherapy for SCLC. Patients who have started therapy with cisplatin and irinotecan, at the dosages mentioned in the protocol, prior to registration can be registered on the trial if done so within 21 days after the start of the first cycle of chemotherapy. Prior palliative radiation therapy will be allowed as long as radiation was completed at least 2 weeks before starting protocol therapy.
3. At least 18 years of age
4. At least one uni-dimensionally measurable lesion or an evaluable outside the field of any prior radiation therapy.

5. Adequate organ function

6. Patients must sign informed consent that details the investigational nature of the study according to the institutional and federal guidelines.

Exclusion Criteria:

1. Symptomatic or history of untreated brain or leptomeningeal metastases. Treated patients should be neurologically stable for 2 weeks after completion of appropriate therapy.
2. Previous or concurrent malignancies, with the exception of adequately treated squamous cell or basal cell carcinoma of the skin, in situ carcinoma of the cervix, or any other malignancy treated and in clinical remission for more than 3 years.
3. Major surgery or radiation therapy within 2 weeks of enrollment.
4. Peripheral neuropathy of NCI grade greater than 2.
5. Symptomatic edema from any etiology.
6. Therapeutic anticoagulation with warfarin. Patients can be eligible if they are changed from warfarin to low molecular weight heparin or heparin at least 2 weeks prior to starting Gleevec.
7. Serious concomitant medical illness, including, but not limited to, uncontrolled congestive cardiac failure, uncontrolled angina, myocardial infarction and/or stroke within 3 months, or HIV infection.
8. Acute or chronic liver disease (e.g., chronic active hepatitis, cirrhosis).
9. History of dementia, active psychiatric disorder or any other condition, considered by the treating physician to impair the patient's ability to take oral pills on a daily basis or comply with the protocol requirements.
10. Pregnant or lactating females. All pre-menopausal and peri-menopausal women should have a negative urine pregnancy test prior to enrollment. All patients, men and women, of reproductive potential should agree to use an effective contraceptive method for the duration of the trial and for 3 months after discontinuation of study treatment.
11. Patients should not participate in other investigational agent study while taking part in this trial.