Inclusion Criteria:

1. Patients with either: a) histologically proven stage I, II, or IIIa NSCLC who have undergone a complete surgical resection of the primary tumor OR b) stage I or II HNSCC who have undergone definitive local treatment (surgery or radiation therapy).
2. HNSCC patients: Definitive local treatment </= 12 months prior to trial enrollment. NSCLC patients: Surgery </= 12 months prior to trial enrollment.
3. No evidence residual cancer
4. Smoking history of at least 10 pack years. May be current or former smoker.
5. Performance status of < = 2 (Zubrod)
6. Age =>18 years
7. Participants must have no contraindications for undergoing bronchoscopy.
8. Patients must have no active pulmonary infections.
9. Participants must not be taking oral non-steroidal anti-inflammatory drugs on a regular basis.
10. Participants must have the following blood levels: total granulocyte count >1500; platelet count > 100,000; total bilirubin < = 1.5 mg. %; and creatinine < = 1.5 mg %.
11. Participants must complete the pretreatment evaluation and must consent to bronchoscopy and to endobronchial biopsy for biomarker studies.
12. All subjects who agree to participate will be given a written and verbal explanation of the study requirements and a consent form that must be signed prior to registration. Subjects will be informed that (a) they must be willing to take capsules daily for the duration of the trial, (b) they must be willing to take biopsies through bronchoscopy and give blood samples at the specified times, (c) they must schedule and keep the specified follow-up visits with their physicians and the study clinics, and (d) side effects and health risks may occur, as described in the informed consent form.
13. Participant must be enrolled in UT MD Anderson Cancer Center protocol #2003-0424 titled "A Phase IIb Vanguard Study Characterizing the Occurrence of Recurrent or Second Primary Tumors in Patients with a Prior History of a Definitively Treated Stage I/II Head and Neck or Non-Small Cell Cancer who are Current or Former Smokers."
14. Patients with prior head and neck cancer only: Participants must have no contraindications for undergoing laryngoscopy.
15. Subject must be considered legally capable of providing his or her own consent for participation in this trial.

Exclusion Criteria:

1. History of radiation therapy to the chest. For those patients with head and neck cancer who received radiation, no more than 10% of the lung volume (apices) may be included.
2. History of systemic chemotherapy. Exception: NSCLC patients may have had up to 4 cycles of platinum-based doublet therapy.
3. Pregnant or breast-feeding (a negative pregnancy test within 72 hours of enrollment for women with child-bearing potential is required)
4. Participants with active gastric or duodenal ulcers or a history of ulcers requiring prophylactic H2 blockers.
5. Participants with active pulmonary infections or recent history of pulmonary infection (within one month).
6. Participants with acute intercurrent illness
7. Participants requiring chronic ongoing treatment with Nonsteroidal anti-inflammatory drugs (NSAIDs). (Casual or non-prescribed use of NSAIDs is permitted as long as their use does not exceed one week at a time.)
8. Participants who are allergic to aspirin or sulfanamides.
9. Patients may not take high dose antioxidants (vitamins E or C) during the study period. "High dose" will be determined by the study investigators.
10. Patients may not take high dose synthetic or natural Vitamin A derivatives (> 10,000 IU per day).
11. History of biologic therapy
12. Women of childbearing potential and men with partners of childbearing potential who are not using an effective method of contraception. Use of contraception will be verified at office visits during first year on study.
13. History of cardiovascular diseases that might include one of the following: myocardial infarction, angina, coronary angioplasty, congestive heart failure, stroke, or coronary bypass surgery.
14. Diagnosis of diabetes
15. History of deep venous thrombosis, pulmonary embolism, systemic lupus erythematosus, family history of protein S or C deficiencies, prior heparin-induced thrombocytopenia, or known Factor V Leiden mutation.
16. Family history of premature CAD. This is defined as individuals with either: 1) father with MI prior to age 55, or 2) mother with MI prior to age 60.