This study plans to learn more about a drug called bexarotene for the treatment of advanced thyroid cancer. Subjects are asked to be in this study because they have thyroid cancer that will not respond to radioactive iodine therapy and shows signs of aggressive behavior.

Bexarotene has been FDA approved for the treatment of a type of skin cancer called cutaneous T-cell lymphoma, but has not been FDA approved for this use. Bexarotene is investigational in the treatment of thyroid cancer.

The purpose of this research study is to test how well the study drug works in humans. The study doctors want to know if:

1. The subjects thyroid cancer gets smaller while you are taking the study drug.
2. The subjects thyroid cancer takes up radioactive iodine better after treatment with the study drug than before treatment.

Inclusion Criteria:

• Subject must have a histologically/cytologically confirmed diagnosis of papillary, follicular, or anaplastic thyroid cancer (any follicular cell derived thyroid cancer).
• Subjects must have evidence of follicular cell-derived thyroid cancer progression. In patients with anatomically stable disease, PET positive lesions will also be eligible given the poor prognostic risk for PET positive thyroid cancer.
• Subjects must not be eligible for surgical resection.
• Subjects must have measurable disease as defined by Response Evaluation Criteria in Solid Tumors (RECIST) criteria.
• Subjects must have laboratory values that fall within certain ranges.
• Subjects must be age 18 years or older.
• Subjects must provide written informed consent prior to any study procedures being performed.
• Females of childbearing potential must have a negative pregnancy test prior to enrollment.
• All eligible subjects must be willing to use adequate contraception throughout the duration of the study.
• Subjects must be willing to submit a primary tumor tissue sample for immunohistochemical analysis.
• Subjects have the option of providing one additional test tube of blood taken at baseline, 6 months and 1 year for banking of plasma for potential future studies (no genetic testing will be conducted). The current planned analysis is for the assessment of a potential peripheral marker for rexinoid responsive cancer - leukemia inhibitory factor (LIF)

Exclusion Criteria:

• Subjects with a known history of hyperlipidemia refractory to treatment.
• Subjects with a known history of hypertriglyceridemia refractory to treatment.
• Subjects with leukopenia below the reference range for the University of Colorado Hospital (UCH) laboratory.
• Subjects, who are pregnant, have a desire to become pregnant or are breastfeeding.
• Subjects who are unwilling or unable to comply with study medication administration, or study guidelines, as determined by the investigator.
• Subjects with any prior history of malignancy with the exception of adequately treated basal cell skin cancer, in situ cervical cancer or other cancer for which the subject has been disease free for 3 years or more.
• Subjects without radiographically assessable disease