To determine the safety and tolerability of galunisertib when combined with Stereotactic Body Radiotherapy (SBRT) (hypofractionated radiation).

Inclusion Criteria:

• Patients must have histologically confirmed hepatocellular carcinoma (HCC) that is inoperable (where surgery is not indicated due to disease extension, co-morbidities or other technical reasons)
• ≥18 years of age and ability to understand and the willingness to sign a written informed consent document. A legally authorized representative signature in the event that the subject is not able to sign themselves is permitted.
• Patients must have either not been eligible for sorafenib therapy, have failed sorafenib therapy, have discontinued sorafenib therapy due to intolerable toxicity or have refused sorafenib
• ECOG performance status ≤2
• Childs Pugh score of ≤7
• Life expectancy of at least 12 weeks
• Must be able to swallow tablets
• Must be willing to comply with protocol procedures (including completion of diaries and outcome measures)
• Local or loco-regional therapy (ie surgery, radiation therapy, hepatic arterial embolization, chemoembolization, radiofrequency ablation, percutaneous ethanol injection or cryoablation) must have been completed ≥4 weeks prior to enrollment
• Must be willing to undergo a pretreatment biopsy
• A history of prior radiotherapy is permitted, as long as the prior radiated site is not overlapping with the site of planned SBRT
• Measurable disease as defined by the Response Evaluation Criteria in Solid Tumors (RECIST) version 1.1
• An index lesion measuring between 1cm-10cm that is amenable to hypofractionated radiation therapy at the discretion of the treating radiation oncologist
• Women of childbearing potential must have a negative serum pregnancy test performed at screening
• Subjects must use an approved contraceptive method (for example, intrauterine device, birth control pills or barrier device) which has an expected failure rate of <1%, if appropriate for at least 3 months after the last dose of galunisertib.

Patients who are HIV-positive are eligible if:

• CD4+ cell count is greater or equal to 250cells/mm3.
• If patient is on retroviral therapy, there must be minimal interactions or -overlapping toxicity of the antiretroviral therapy with the experimental cancer treatment.
• No history of non-malignancy AIDS defining conditions other than low CD4+ count.
• Probable long-term survival with HIV if cancer were not present.
• Must have adequate organ and hematopoietic function as defined below:

Laboratory Test Required Value Absolute neutrophil count ≥1.5 x 10^9/L Platelet count ≥100 x 10^9/L Hemoglobin ≥9.0 x 10^9/L Alanine transaminase ≤2.5 x ULN Aspartate aminotransferase ≤2.5 x ULN Serum creatinine or CrCl ≤2.0 x ULN Total Bilirubin ≤1.5 x ULN

Exclusion Criteria:

• Any history of a serious medical or psychiatric condition that would prevent the patient from signing the informed consent form
• Pregnant or breastfeeding women.
• Use of any other chemotherapy, radiotherapy or experimental drug within 4 weeks prior to first study treatment date
• A history of radiotherapy that, in the opinion of the investigator, would render SBRT unsafe to administer
• Those who have not recovered from adverse events ≤ grade 1 secondary to therapy administered >4 weeks prior to first study treatment date, with the exception of stable grade 2 neuropathy
• Subjects may not receive concomitant anticancer agents. Antiviral agents aimed at treating infectious hepatitis are permitted
• History of or suspected hypersensitivity to radiation or to galunisertib
• Uncontrolled ascites
• Subjects with a history of or evidence of cardiac disease during screening, defined as any one of the following: myocardial infarction within 6 months prior to study entry, unstable angina pectoris, New York Heart Association Class III/IV congestive heart failure, uncontrolled hypertension.
• Subjects with a documented major ECG abnormalities (not responding to medical treatments) or not clinically stable for at least 6 months.
• Subjects with major abnormalities documented by ECHO with Doppler (for example, moderate or severe heart valve function defect) that is not stable for at least 6 months.. Note: Left ventricular [LV] ejection fraction <50% is allowed only if clinically stable for at least 6 months (evaluation based on the institutional lower limit of normal).
• Subjects with a predisposition toward developing aneurysms of the ascending aorta or aortic stress including a family history of aneurysms, Marfan Syndrome, Ehlers Danlos Type IV, bicuspid aortic valve or evidence of damage to the large vessels of the heart documented by previously obtained or screening CT scan/MRI
• Subjects with uncontrolled brain metastases. Subjects with brain metastases must have stable neurological status following local therapy (surgery or radiation) for at least 4 weeks prior to first study treatment and must be off steroids
• Any concurrent condition requiring the continued or anticipated use of systemic steroids beyond physiologic replacement dosing (excluding non-systemic inhaled, topical skin and/or eye drop-containing corticosteroids) or immunosuppressive therapy (excludes low-dose methotrexate). All other systemic corticosteroids above physiologic replacement dosing must be discontinued at least 4 weeks prior to first study treatment
• Active drug or alcohol use or dependence as documented in the chart that, in the opinion of the investigator, would interfere with adherence to study requirements
• A second primary malignancy that, in the judgment of the investigator, may affect the interpretation of results
• Prior malignancies. Patients with carcinoma in-situ of any origin and patients with prior malignancies who are in remission and whose likelihood of recurrence is very low (such as basal cell carcinoma) as judged by the Lilly clinical research physician (CRP), are eligible.
• Any illness or condition that in the opinion of the investigator may affect the safety of the subject or the evaluation of any study endpoint
• Any other conditions judged by the investigator that would limit the evaluation of the subject