Procurement Eligibility  Inclusion Criteria:  Relapsed or refractory GPC3-positive* hepatocellular carcinomas (as determined by immunohistochemistry with an extent score of >=Grade 2 [>25% positive tumor cells] and an intensity score of >= 2 [scale 0-4]). Age ≥18 years Lansky or Karnofsky score ≥60% Life expectancy ≥16 weeks Barcelona Clinic Liver Cancer Stage A, B or C (for patients with hepatocellular carcinoma only) Child-Pugh-Turcotte score <7 (for patients with hepatocellular carcinoma only) Informed consent explained to, understood by and signed by patient/guardian. Patient/guardian given copy of informed consent  Exclusion Criteria:  History of hypersensitivity reactions to murine protein-containing products OR presence of human anti-mouse antibody (HAMA) prior to enrollment (only patients who have received prior therapy with murine antibodies). History of organ transplantation Known HIV positivity Active bacterial, fungal or viral infection (except Hepatitis B or Hepatitis C virus infections)  Treatment Eligibility  Inclusion Criteria:  Age ≥ 18 years Barcelona Clinic Liver Cancer Stage A, B or C (for patients with hepatocellular carcinoma only) Life expectancy of ≥ 12 weeks Lansky or Karnofsky score ≥ 60% Child-Pugh-Turcotte score < 7 (for patients with hepatocellular carcinoma only)  Adequate organ function:  Creatinine clearance as estimated by Cockcroft Gault or Schwartz ≥ 60 ml/min serum AST< 5 times ULN total bilirubin < 3 times ULN for age INR ≤1.7 (for patients with hepatocellular carcinoma only) absolute neutrophil count > 500/μl platelet count > 25,000/μl (can be transfused) Hgb ≥ 7.0 g/dl (can be transfused) Pulse oximetry >90% on room air Refractory or relapsed disease after treatment with up- front therapy and at least one salvage treatment cycle Recovered from acute toxic effects of all prior chemotherapy and investigational agents before entering this study Sexually active patients must be willing to utilize one of the more effective birth control methods for 3 months after the T-cell infusion. Informed consent explained to, understood by and signed by patient/guardian. Patient/guardian given copy of informed consent  Exclusion Criteria:  Pregnancy or lactation Uncontrolled infection Systemic steroid treatment (≥ 0.5 mg prednisone equivalent/kg/day, dose adjustment or discontinuation of medication must occur at least 24hrs prior to CAR T cell infusion) Known HIV positivity Active bacterial, fungal or viral infection (except Hepatitis B or Hepatitis C virus infections) History of organ transplantation History of hypersensitivity reactions to murine protein-containing products OR presence of human anti-mouse antibody (HAMA) prior to enrollment (only patients who have received prior therapy with murine antibodies)