Inclusion Criteria

- INCLUSION CRITERIA:

2.1.1.1 Patients must have histopathological confirmation of hepatocellular carcinoma
(HCC) by the Laboratory of Pathology of the NCI prior to entering this study OR
histopathological confirmation of carcinoma in the setting of clinical and radiological
characteristics which, together with the pathology, are highly suggestive of a diagnosis
of HCC. Fibrolammelar variant is also allowed.

2.1.1.2 Patients must have disease that is not amenable to potentially curative resection,
transplantation or ablation. For Cohort A patients must have progressed on or been
intolerant of prior sorafenib therapy.

2.1.1.3 Disease must be technically amenable to transhepatic arterial chemoembolization
(TACE) or radiofrequency ablation (RFA). Each case will be discussed at GI tumor board
with interventional radiology. Patients must have evaluable disease.

2.1.1.4 If liver cirrhosis is present, patient must have a Child-Pugh A/B7 classification.

2.1.1.5 Age greater than or equal to 18 years

2.1.1.6 Life expectancy of greater than 3 months.

2.1.1.7 ECOG performance status 0-2.

2.1.1.8 Patients must have normal organ and marrow function as defined below:

- leukocytes greater than or equal to 3,000/mcL

- absolute neutrophil count greater than or equal to 1,000/mcL

- platelets greater than or equal to 60,000/mcL

- total bilirubin, If cirrhosis present: Part of Child Pugh requirement. If no
cirrhosis: Bili should be less than or equal to 2 times ULN

- Serum albumin, If cirrhosis present: Part of Child Pugh requirement. If no cirrhosis:
albumin should be greater than or equal to 2.5g/dl

- Patients are eligible with ALT or AST up to 5 times ULN.

- creatinine, less than 1.5 times institution upper limit of normal

OR

-creatinine clearance greater than or equal to 45 mL/min/1.73 m(2), as calculated below,
for patients with creatinine levels above institutional normal

2.1.1.9 Patients must have recovered from any acute toxicity related to prior therapy,
including surgery. Toxicity should be less than or equal to grade 1 or returned to
baseline.

2.1.1.10 Patients must not have other invasive malignancies within the past 5 years (with
the exception of non-melanoma skin cancers, non-invasive bladder cancer or localized
prostate cancer for whom systemic therapy is not required).

2.1.1.11 Patient must be able to understand and willing to sign a written informed consent
document.

EXCLUSION CRITERIA:

2.1.2.1 Patients who have had standard of care chemotherapy, large field radiotherapy, or
major surgery must wait 2 weeks prior to entering the study. For recent experimental
therapies a 28 day period of time must elapse before treatment.

2.1.2.2 Patients who have undergone prior liver transplantation are ineligible.

2.1.2.3 Patients with known brain metastases will be excluded from this clinical trial
because of their poor prognosis and because they often develop progressive neurologic
dysfunction that would confound the evaluation of neurologic and other adverse events.

2.1.2.4 Uncontrolled intercurrent illness including, but not limited to, ongoing or active
systemic infection, symptomatic congestive heart failure, unstable angina pectoris,
cardiac arrhythmia or psychiatric illness/social situations that would limit compliance
with study requirements.

2.1.2.5 History of chronic autoimmune disease (e.g., Addison's disease, multiple
sclerosis, Graves' disease, Hashimoto's thyroiditis, rheumatoid arthritis, hypophysitis,
etc.) with symptomatic disease within the 3 years before randomization. Note: Active
vitiligo or a history of vitiligo will not be a basis for exclusion.

2.1.2.6 Dementia or significantly altered mental status that would prohibit the
understanding or rendering of Information and Consent and compliance with the requirements
of the protocol.

2.1.2.7 Diverticulitis (either active or history of) within the past 2 years. Note that
diverticulosis is permitted.

2.1.2.8 Active or history of inflammatory bowel disease (colitis, Crohn's), irritable
bowel disease, celiac disease, or other serious, chronic, gastrointestinal conditions
associated with diarrhea. Active or history of systemic lupus erythematosus or Wegener's
granulomatosis.

2.1.2.9 Currently receiving immunosuppressive doses of steroids or other immunosuppressive
medications (inhaled and topical steroids are permitted)

2.1.2.10 History of sarcoidosis syndrome

2.1.2.11 Patients should not be vaccinated with live attenuated vaccines within 1 month of
starting Tremelimumab treatment.

2.1.2.12 HIV-positive patients receiving anti-retroviral therapy are excluded from this
study due to the possibility of pharmacokinetic interactions between antiretroviral
medications and Tremelimumab. HIV positive patients not receiving antiretroviral therapy
are excluded due to the possibility that Tremelimumab may worsen their condition and the
likelihood that the underlying condition may obscure the attribution of adverse events.

2.1.2.13 History of hypersensitivity reaction to human or mouse antibody products.

2.1.2.14 Pregnancy and breast feeding are exclusion factors. The effects of Tremelimumab
on the developing human fetus are unknown. Enrolled patients must agree to use adequate
contraception (hormonal or barrier method of birth control; abstinence) prior to study
entry, the duration of study participation and 3 months after the end of the treatment.
Should a woman become pregnant or suspect she is pregnant while she or her partner is
participating in this study, she should inform her treating physician immediately.

2.1.2.15 Patients with unhealed surgical wounds for more than 30 days.