Primary Phase I:To determine dose limiting toxicities and maximum tolerated dose (MTD) of the oral administration of hydroxychloroquine (HCQ) in conjunction with transarterial chemoembolization (TACE) in treating hepatocellular carcinoma (HCC). A conventional 3+3 design will be utilized. Primary Phase II: To evaluate the complete response rate in a cohort of patients treated at the MTD, A Simon's Optimal Two-stage design will be utilized.