Inclusion Criteria:

- Histologically confirmed thyroid cancer

- One of the following subtypes:

- Papillary thyroid cancer

- Follicular thyroid cancer

- Hürthle cell thyroid cancer

- Insular thyroid cancer

- Medullary thyroid cancer

- Mixed histology thyroid cancer

- Poorly differentiated thyroid cancer

- Tall-cell thyroid cancer

- Metastatic and/or locally advanced or locally recurrent disease

- Measurable disease, defined as ≥ 1 unidimensionally measurable lesion ≥ 20 mm by
conventional techniques OR ≥ 10 mm by spiral CT scan

- Lesions in a previously irradiated area allowed provided there has been
subsequent disease progression of the irradiated lesions

- The following are not considered measurable disease:

- Bone lesions

- Leptomeningeal disease

- Ascites

- Pleural or pericardial effusion

- Lymphangitis cutis/pulmonis

- Abdominal masses not confirmed and followed by imaging techniques

- Cystic lesions

- Not a candidate for radioactive iodine I^131 therapy

- Performance status - ECOG 0-1

- At least 6 months

- WBC ≥ 3,000/mm^3

- Absolute neutrophil count ≥ 1,500/mm^3

- Platelet count ≥ 100,000/mm^3

- Bilirubin ≤ 1.5 mg/dL

- AST and ALT ≤ 2.5 times upper limit of normal

- Creatinine ≤ 1.5 mg/dL

- Not pregnant or nursing

- Negative pregnancy test

- Fertile patients must use effective contraception

- No history of allergic reaction attributed to compounds of similar chemical or
biologic composition to study drug

- No ongoing or active infection

- No psychiatric illness or social situation that would preclude study compliance

- No other uncontrolled illness

- No other active malignancy except nonmetastatic nonmelanoma skin cancer or carcinoma
in situ of the cervix

- More than 4 weeks since prior systemic cytotoxic chemotherapy (6 weeks for
nitrosoureas or mitomycin)

- No more than 2 prior chemotherapy regimens for the treatment of thyroid cancer

- See Disease Characteristics

- More than 4 weeks since prior external beam radiotherapy

- At least 24 weeks since prior radioactive iodine I^131 therapy

- Recovered from prior therapy

- More than 4 weeks since prior valproic acid or any other histone deacetylase
inhibitor

- More than 4 weeks since prior investigational tumor-specific therapy

- Concurrent oral or IV bisphosphonates for bony metastases allowed at the discretion
of the investigator

- No concurrent combination antiretroviral therapy for HIV-positive patients

- No other concurrent tumor-specific or investigational therapy

- No other concurrent anticancer therapy

- No concurrent adjuvant therapy for another cancer