The purpose of this study is to try to improve the odds that your cancer may be cured. Pemetrexed and cisplatin are traditional chemotherapy drugs that have been shown to help some patients with non-small cell lung cancer. Many different types of cancer cells, including your type of lung cancer, have a protein on their surface called the epidermal growth factor receptor (EGFR). Stimulation of these receptors can result in growth of cancer cells and progression of cancer. In addition, your cancer has an EGFR mutation (a specific abnormality in the genetic code for EGFR). Erlotinib (TarcevaTM) is a newer drug which has shown benefit for patients with lung cancers that contain an EGFR mutation. Erlotinib works by blocking this receptor and depriving the cancer cells of this message to grow and multiply. In this research study, we plan to combine erlotinib with traditional chemotherapy drugs to see if the combination works better than chemotherapy alone.