This is a Phase II trial of neoadjuvant chemotherapy with paclitaxel, carboplatin and gemcitabine in the treatment of locally advanced transitional cell carcinoma of the bladder. Patients will be stratified based on extent of disease. Patients with T3, N0 disease will receive 3 cycles of chemotherapy and then proceed to cystectomy. Patients with T4 disease or any patient with N1-3 disease will receive 3 cycles of therapy followed by assessment of response. Patients with evidence of response will then receive an additional three cycles of therapy with reassessment of resectability after cycles #6. Correlative Studies: Tumor specimens obtained at initial biopsy will be assayed for expression of p53, Rb and p21.