- Cytologically or histologically confirmed advanced or metastatic HCC. If no histological diagnosis, patient must have imaging studies compatible with HCC. - Age 18 years and above - ECOG performance status of 0 or 1 - Not a candidate for curative treatments (i.e., resection, transplantation) - Child-Pugh class A or B7 liver function - Measurable disease as defined by RECIST 1.1 - Patients who received prior local therapy (e.g., TACE) are eligible. - Documented virology status of hepatitis, as confirmed by screening HBsAg, anti-HBc, and/or anti-HCV - Life expectancy> 3 months - For women who are not postmenopausal (12 months of amenorrhea) or surgically sterile (absence of ovaries and/or uterus): agreement to use two adequate methods of contraception. For men: agreement to use a barrier method of contraception during the treatment period - Hematologic, Biochemical, and Organ Function within 7 days prior to Cycle 1 Day 1: Granulocyte count > 1500/mm3, Platelet count > 75,000/ mm3, Hemoglobin > 8 g/dL; Total bilirubin < 2.0; Albumin > 2.8g/dl; AST (SGOT) and ALT (SGPT) < 5 x ULN; Serum creatinine< 1.5 x ULN - Cohort 1 (with sorafenib): No previous systemic therapy including sorafenib or chemotherapy treatment. Previous TACE and local treatments are permitted. - Cohort 2 (on progression of sorafenib): Patients who have received prior sorafenib therapy for at least 4 weeks and has confirmation of disease progression on CT/MRI. Prior surgery or local therapy within 4 weeks prior to Cycle 1 Day 1, with the exception of palliative radiation therapy to the bone

- Patients receiving prior therapy with HCQ. - Patients with uncontrolled brain metastases. Patients with brain metastases must be asymptomatic and off corticosteroids for at least one week. - Due to risk of disease exacerbation, patients with psoriasis are ineligible unless the disease is well controlled, and they are under the care of a specialist for the disorder who agrees to monitor the patient for exacerbations. - Patients with previously documented macular degeneration or or untreated diabetic retinopathy (stable retinopathy is allowed). - Patients may not be receiving any other investigational agents. - History of allergic reactions attributed to compounds of similar chemical or biologic composition to HCQ. - Patients requiring the use of enzyme-inducing anti-epileptic medication (phenytoin, carbamazepine, phenobarbital, primidone or oxcarbazepine) are not eligible for entry into the study. - Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements - QTc > 500 milliseconds (ms) at baseline. - Gastrointestinal tract disease resulting in an inability to take oral medication or a requirement for IV alimentation, prior surgical procedures affecting absorption, or active peptic ulcer disease. Patients with NG-tube, J-tube, or G-tube will not be allowed to participate. - Pregnant women are excluded from this study because sorafenib has the potential for teratogenic or abortifacient effects. For this reason, women of childbearing potential and men must also agree to use adequate contraception (hormonal or barrier method of birth control) prior to study entry and for the duration of study participation. - Should a woman become pregnant or suspect she is pregnant while participating in this study, she should inform her treating physician immediately. Because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with sorafenib, breastfeeding should be discontinued. - Informed Consent - No study specific procedures will be performed without a written and signed informed consent document. Patients who do not demonstrate the ability to understand or the willingness to sign the written informed consent document will be excluded from study entry.