This is a Phase 2 study of pemetrexed and gemcitabine chemotherapy given once every 14 days to patients with advanced stage non-small cell lung cancer. This treatment is for patients that have not received any prior chemotherapy treatment for lung cancer. The primary goal is to find out if the tumor gets smaller or disappears with this treatment.

Inclusion Criteria:

1. Have a diagnosis of advanced stage non-small cell lung cancer.
2. Are able to be active at home and/or work.
3. Have not received chemotherapy for this cancer disease.
4. Have good organ function (for example, most blood work is normal).
5. Have completed any prior radiation treatment at least 4 weeks ago.

Exclusion Criteria:

1. Have been treated with an investigational/research drug within the last month.
2. Have cancer that has spread to the brain and is causing symptoms.
3. Have an active infection or other serious medical condition.
4. Have a second cancer in addition to non-small cell lung cancer.
5. Can not stop taking aspirin or other anti-inflammatory agents for 5-8 days.