Study treatment will be divided into 5 stages:

      Stage 1-induction, consisting of afatinib for two 4-week cycles. Afatinib is a pill that the
      patient takes by mouth once per day. The patient will receive a study drug diary in which to
      record the doses of afatinib.

      Stage 2-concurrent radiation and chemotherapy with cisplatin/pemetrexed for two 3-week
      cycles.

      Stage 3-Surgery to remove tumor for participants whose tumor can be removed by surgery. This
      will be done about 4-6 weeks after finishing radiation and chemotherapy. The exact timing
      will depend upon how quickly the patient recovers from side effects of the radiation and
      chemotherapy. The investigators will use a piece of the patients tumor removed by surgery for
      research tests to look for biomarkers such as genes and proteins that may be associated with
      response to afatinib, chemotherapy or radiation.

      Stage 4-Chemotherapy after surgery (adjuvant chemotherapy). The patients doctor will decide
      if the patient will receive chemotherapy after the patients surgery but before receiving
      consolidation with afatinib. If the patient does receive this, it will start 6-12 weeks after
      surgery or finishing radiation if the patient does not have surgery. The chemotherapy will be
      the same as that received along with the radiation therapy.

      Stage 5-Consolidation with afatinib for twenty-six 4-week cycles (2 years) for participants
      who responded to the 2 cycles of induction afatinib.

      The investigators would like to keep track of the patients medical condition and status of
      the patients disease for up to 5 years after the patient stops study treatment. Keeping in
      touch with the patients and checking on the patients condition every year helps the
      investigators look at the long-term effects of the research study. The patients will be asked
      to have CT scans as follows:

        -  Every 3 months for the first year after stopping study treatment

        -  Every 6 months for years 2-4 after stopping study treatment

        -  Once per year in year 5 after stopping study treatment