Inclusion Criteria:

          1. Patients must have histologically confirmed thyroid carcinoma with the PAX8-PPARgamma
             translocation (translocation testing will be performed on archived tissue during the
             screening period).

             Refractory to radioactive iodine (RAI) as defined by: the tumor does not concentrate
             RAI; or the patient has had RAI within the last 16 months and has had progression
             despite that RAI; or the last RAI treatment was >16 months ago and the patient
             progressed after at least two RAI treatments; or the patient has received RAI
             treatments with a cumulative RAI dose of ≥22.2 GBq (600 mCi)

             Not a candidate for surgery or RAI therapy with curative intent.

             Lesions that would be treated by external beam radiation therapy (EBRT) based on
             standard of care can be so treated, but then cannot be used as target lesions.

          2. Measurable disease by RECIST 1.1 criteria.

          3. Documented disease progression by RECIST 1.1 in the past 14 months.

          4. Availability of histological material (primary tumor or metastases) for review of the
             diagnosis and demonstration of PAX8-PPARgamma fusion gene.

          5. Adequate TSH suppression (<0.5 mIU/L)

          6. Prior chemotherapy or surgery must have been completed at least 28 days prior to
             registration, and all toxicities must have resolved.

          7. Prior radioactive iodine must have been completed at least 6 months prior to
             registration, or there must be documented disease progression since such therapy if it
             was within 6 months. Sites that have received EBRT must have disease progression
             post-EBRT to be used as sites of measurable disease.

          8. Life expectancy of greater than 6 months.

          9. ECOG performance status 2 or less.

         10. Patients must have normal organ function as defined below:

             AST(SGOT)/ALT(SGPT) less than 2.5 X institutional upper limit of normal (within 1
             month of study Day 1)

         11. Patients must be able to consume oral medications.

         12. Women of childbearing potential must have a negative pregnancy test at baseline prior
             to receiving any study drug and must practice effective contraception while on study.
             (Pregnant or lactating patients are excluded).

         13. All patients must sign an informed consent prior to enrollment.

        Exclusion Criteria:

          1. Patients may not be receiving any other investigational agents.

          2. Patients with known untreated brain metastases.

          3. History of allergic reactions attributed to compounds of similar chemical or biologic
             composition to pioglitazone.

          4. Diagnosis of diabetes mellitus or current therapy with any drugs used to treat
             diabetes mellitus, including but not limited to insulin, sulfonylureas, metformin,
             rosiglitazone (Avandia), and pioglitazone (Actos) within 14 days of study Day 1

          5. Therapy with rosiglitazone (Avandia) or pioglitazone (Actos) at any time since the
             diagnosis of thyroid cancer.

          6. Uncontrolled intercurrent illness including, but not limited to, ongoing or active
             infection, congestive heart failure, unstable angina pectoris, or cardiac arrhythmias.

          7. Pregnant women are excluded from this study because pioglitazone is a U.S. Food and
             Drug Administration Pregnancy Category C drug. Because there is an unknown but
             potential risk for adverse events in nursing infants secondary to treatment of the
             mother with pioglitazone, breastfeeding should be discontinued if the mother is
             treated with pioglitazone.

          8. No concurrent radiotherapy or chemotherapy may be given to the patient during the
             administration of the study drug.

          9. Patients with uncontrolled malabsorption syndromes.

         10. Patients with a history of congestive heart failure of any New York Heart Association
             class.

         11. Any medical or psychiatric illness which, in the opinion of the principal
             investigator, would compromise the patient's ability to tolerate this treatment
             regimen.

         12. Use of rifampin (strong CYP2C8 inducer) within 14 days of study Day 1.

         13. Other current malignancy than the disease under study.

         14. Grade 2 or worse edema within 14 days of study Day 1, per CTCAE v4.