Patients receive trastuzumab (Herceptin) IV over 30-90 minutes on days 1, 8, and 15; paclitaxel IV over 3 hours and carboplatin IV over 15 minutes on day 1; and gemcitabine IV over 30 minutes on days 1 and 8. Courses repeat every 3 weeks. Patients achieving a complete response (CR) receive 3 courses past CR. Patients achieving a partial response or stable disease continue on therapy until CR or disease progression or unacceptable toxicity.