The purpose of this study is to compare any good and bad effects patients may have when treated with the standard treatment against patients who are treated with the standard treatment plus erlotinib (an investigational drug). Patients with early stage non-small cell lung cancer that was surgically removed and may have been treated with chemotherapy and/or radiation will be considered for participation. The tumor removed has a mutation of a gene called EGFR (Epidermal Growth Factor Receptor). We are trying to find out if this mutation could help us make decisions about which type of treatment is best for this type of cancer. People not in a research study are usually not treated with anything after they finish their chemotherapy although some of them may receive radiation therapy.