Patients receive oral erlotinib alone daily on weeks 1 and 2. Patients then receive oral erlotinib daily beginning on day 1 and docetaxel IV over 1 hour on day 3 of weeks 3-9. Patients also undergo radiotherapy once daily 5 days a week on weeks 3-9. Patients continue erlotinib for up to 2 years in the absence of disease progression or unacceptable toxicity. Patients who had N2 or greater cervical lymph node involvement at baseline or have residual neck adenopathy after chemoradiotherapy undergo neck dissection 6-8 weeks after completion of chemoradiotherapy. Erlotinib is held for 1 week before planned surgery and until healing is complete.