Anaplastic thyroid carcinoma (ATC) is a high-grade neoplasm, characterized by an aggressive clinical course with brief survival, and refractoriness to currently available local and systemic modalities of treatment. There is no standard therapy for ATC, and no randomized comparative trials have been known to be conducted in this disease. One potential strategy is to combine the anti-tumor activity of the vascular disrupting agent combretastatin with conventional cytotoxic agents. This study will compare the overall survival of ATC patients treated with the triplet combination of combretastatin, paclitaxel, and carboplatin compared with the doublet treatment of paclitaxel and carboplatin.