Inclusion Criteria:

• Patients must have anaplastic thyroid carcinoma histologically or cytologically confirmed by a pathology review.
• Patients may have been refractory to or progressed during or after therapy, or relapsed within 6 months following initial combined modality therapy (usually including systemic chemotherapy and radiation) for regionally advanced disease.
• Where patients have received combined modality therapy for metastatic disease, systemic therapy is limited to one chemotherapy regimen that is clearly administered contiguously, (i.e., in an uninterrupted primary therapeutic approach). Patients who receive chemotherapy for metastatic disease after a combined modality approach are ineligible.
• In patients having received prior radiation, 3 weeks must have elapsed since radiation and disease must be present beyond radiation ports.
• A minimum of 3 weeks must have elapsed from the time a patient last received chemotherapy prior to the first dose of study drug (6 weeks for therapy known to be associated with delayed toxicity such as nitrosureas or mitomycin-C).
• Patients with bulky thyroid/neck masses and/or suspicion of airway obstruction must undergo screening (indirect and direct laryngoscopy) to ensure patency of the trachea/airway prior to study enrollment and treatment.
• Patients must be greater than or equal to 18 years of age.
• Patients must have an Eastern Cooperative Oncology Group (ECOG) Performance Score less than or equal to 2.
• Life expectancy greater than or equal to 12 weeks.
• Patients must have adequate bone marrow reserve as evidenced by:

Absolute neutrophil count (ANC) greater than 1,500/microL. Platelet count greater than 75,000/microL.

• Patients must have adequate renal function as evidenced by serum creatinine less than or equal to 2.0 mg/dL (less than 177 micromol/L).
• Patients must have adequate hepatic function as evidenced by:

Serum total bilirubin less than 2X greater than the upper limit of normal (ULN) (less than3X ULN in patients with liver metastases).

AST (aspartate aminotransferase)/ALT (alanine aminotransferase) less than or equal to 3X the ULN for the local reference lab (less than or equal to 5X the ULN for patients with liver metastases).

• Patients or their legal representatives must be able to read, understand and provide written informed consent to participate in the trial.
• Patients must have no clinically important sequelae from any prior surgery or radiotherapy.
• All women of childbearing potential must have a negative serum pregnancy test.
• Women of childbearing potential as well as fertile men and their partners must agree to use an effective form of contraception during the study and for 90 days following the last dose of study medication. (An effective form of contraception is an oral contraceptive or a double barrier method.)

Exclusion Criteria:

• Patients with tumors confined to the thyroid.
• Patients with an uncontrolled active infection.
• Clinically evident brain metastasis, including symptomatic involvement, evidence of cerebral edema by CT or MRI, radiographic evidence of progression of brain metastasis since definitive therapy, or continued requirement for corticosteroids.
• Patients who receive chemotherapy for metastatic disease after completion of a combined modality approach.
• Patients with history of malignancies other than ATC except patients with curatively treated basal cell carcinoma of the skin, cervical intra-epithelial neoplasia, or localized prostate cancer with a current PSA of less than 4.0 mg/dL or microg/L. (Patients with other curatively treated malignancies who have no evidence of metastatic disease will be considered after discussion with the Medical Monitor.)
• Patients with known hypersensitivity to CA4P, paclitaxel or carboplatin, or any of their components.
• Patients who are receiving concurrent investigational therapy or who have received investigational therapy for any indication within 28 days of the first scheduled day of dosing. (Investigational therapy is defined as treatment for which there is currently no regulatory authority approved indication.)
• Patients with greater than Grade 2 peripheral neuropathy.
• Patients who are pregnant or lactating.
• Patients with a history of prior cerebrovascular event, including transient ischemic attack.
• Patients with uncontrolled hypertension defined as blood pressure greater than 150/100 mm Hg despite medication.
• Patients with symptomatic vascular disease (e.g. intermittent claudication)
• Patients with a history of unstable angina pectoris pattern, myocardial infarction (including non-Q wave MI) within the past 6 months, or NYHA Class III and IV congestive heart failure.
• Patients with a history of torsade de pointes.
• Patients with bradycardia (less than 60 b/m), heart block (excluding 1st degree block, being PR interval prolongation only), and congenital long QT syndrome.
• Patients with any ventricular arrhythmias, or new ST segment elevation or depression or Q wave on ECG.
• Patients with ejection fractions less than normal (i.e. less than 45%).
• Patients with QTc prolongation greater than 450 ms.
• Patients requiring any drugs known to prolong the QTc interval, including anti-arrhythmic medications.
• Patients with potassium concentrations below 4.0 mEq/dL and magnesium concentrations below 1.8 mg/dL despite being on an electrolyte supplement.
• Patients requiring any drugs known to prolong the QTc interval.
• Patients with any other intercurrent medical condition, including mental illness or substance abuse, deemed by the Investigator to be likely to interfere with a patient's ability to sign informed consent, cooperate and participate in the study, or interfere with the interpretation of the results.
• Patients with a history of solid organ transplant or bone marrow transplant.