Inclusion Criteria

Inclusion

- Diagnosis of hepatocellular carcinoma (HCC): The diagnosis of HCC may be based upon
pathological or clinical criteria (Clinical diagnosis requires a history of
cirrhosis, chronic hepatitis B infection, or non-alcoholic hepatosteatosis (NASH)
and, for imaging abnormalities 1 to 2 cm in diameter, classic enhancement by at least
two of three imaging techniques (computed tomography, Magnetic resonance imaging,
Ultrasound), or, for imaging abnormalities > 2cm, classic enhancement by at least one
imaging technique and an alpha-fetoprotein (AFP) > 200 ng/mL

- Performance status Eastern Cooperative Oncology Group (ECOG) equal or less than 2

- If cirrhosis, Child-Pugh classification A or B

- Total bilirubin =< 3.0 mg/dL

- Creatinine =< 1.5 x upper institutional limit

- prothrombin (PT)/international normalized ratio (INR) =< 1.7 (if not due to
anticoagulants)

- absolute neutrophil count (ANC) >= 1.5

- Platelets >= 60,000

- hemoglobin (Hgb) >= 8.5 (transfusion or erythropoietin-like substances not permitted)

- Any prior therapies such as surgery, chemoembolization, radiofrequency ablation, and
alcohol injection are allowed as long as toxicity from prior therapy is =< grade 1
(Prior sorafenib is allowed, and patients must be on a stable tolerable dose prior to
enrollment; if it is known that the patient tolerates standard dose sorafenib (400 mg
orally twice daily), then they will enroll in cohort A; if they tolerate reduced dose
sorafenib (200 mg orally twice daily), then they will enroll in cohort B;
participation in an additional research imaging study is permissible, imaging for
this study will be evaluated independently)

- Measurable or evaluable disease by Response Evaluation Criteria in Solid Tumors
(RECIST) criteria or elevated AFP

- Ability to understand and willingness to sign a written informed consent (A signed
informed consent must be obtained prior to any study specific procedures)

- Women of childbearing potential must have a negative pregnancy test performed within
7 days prior to the start of treatment (Women of childbearing potential and men must
agree to use a medically accepted form of birth control for the duration of study
participation; Men must agree to use a medically accepted form of birth control for 4
months following completion of study treatment)

Exclusion

- Candidate for surgical resection, orthotopic liver transplantation

- Known central nervous system metastasis

- Any investigational agent within 4 weeks or 5 half-times, whichever is longer, of
first dose of study treatment

- Known or presumed intolerance of sorafenib or vorinostat

- Unable to swallow medication

- Suspected malabsorption

- Active illicit substance or alcohol abuse

- Contraindication to antiangiogenic agents, including: Pulmonary hemorrhage/bleeding
event >= Grade 2 within 4 weeks of first dose of study drug; Any other
hemorrhage/bleeding event >= Grade 3 within 4 weeks of first dose of study treatment;
serious non-healing wound, ulcer, or bone fracture.

- Thrombolic or embolic events such as a cerebrovascular accident including transient
ischemic attacks within the past 6 months

- Major cardiac dysfunction, such as uncontrolled angina, congestive heart failure with
New York Heart Association (NYHA) class III or higher, known left ventricular
ejection fraction less than 40%

- Systolic blood pressure > 160 mmHg or diastolic pressure > 90 mmHg despite optimal
medical management

- Significant lung disease (oxygen saturation less than 88% in room air)

- Serious uncontrolled infection; known human immunodeficiency virus
(HIV)-seropositivity requiring retroviral therapy, or diagnosis of acquired immune
deficiency syndrome (AIDS); diagnosis of chronic hepatitis B or C allowed

- Other condition(s) that in the opinion of the investigator might compromise the
objectives of the study