Inclusion Criteria:
* Women (or male with inflammatory HCA considered as non resectable whatever the size of the HCA)
* Written informed consent for participation in study
* Histologically proven hepatocellular adenoma (confirmed by a centralized reviewing) with available FFPE
* At least one HCA of inflammatory subtype confirmed at histology and immunohistochemistry (CRP or SAA immunohistochemistry) by a centralized reviewing
* At least one HCA of more than 5 cm at imaging of inflammatory subtype (if the HCA of more than 5 cm is not the same HCA proved as inflammatory at histology this HCA should harbored the same imaging features than the HCA with available histology) for women.
* Diagnosed at histology over the last 5 years
* Absence of desire of pregnancy while treated by baricitinib and for at least 4 weeks following the last dose of investigational product
* Females of childbearing potential should have a contraception (without estrogen) when engaging in sexual intercourse with a male partner while treated by baricitinib and for at least 4 weeks following the last dose of investigational product. In case of oral contraception, patients should have been using it for a minimum of one month before the beginning of the treatment. A woman is considered of childbearing potential (WOCBP), i.e. fertile, following menarche and until becoming post-menopausal unless permanently sterile. Permanent sterilization methods include hysterectomy, bilateral salpingectomy and bilateral oophorectomy. A postmenopausal state is defined as no menses for 12 months without an alternative medical cause.
* Male when engaging in sexual intercourse with a female partner shoud have a contraception while treated by baricitinib and for at least 4 weeks following the last dose of investigational product A man is considered fertile after puberty unless permanently sterile by bilateral orchiectomy
* Past infection of Varicella zona Virus confirmed by serology or vaccine against Varicella zona Virus done more than 4 weeks before the inclusion
* Coverage for medical insurance
Exclusion criteria:
* \< 18 years old and \> 65 years old
* Pregnancy or breastfeeding woman
* Ongoing estrogen-based contraception at inclusion
* Patient on AME (state medical aid)
* Have a current or recent (\<4 weeks prior to inclusion) clinically serious viral, bacterial, fungal, or parasitic infection (Note: For example, a recent viral upper respiratory tract infection or uncomplicated urinary tract infection should not be considered clinically serious).
* Have screening electrocardiogram (ECG) abnormalities that, in the opinion of the investigator or the sponsor, are clinically significant and indicate an unacceptable risk for the patient's participation in the study.
* Thrombocytopenia \< 100 000/mm3
* Neutropenia \< 1200/mm3
* Lymphopénia \< 750/mm3
* Anemia \< 9 g/dl
* Concomitant use of immunosuppressive treatment such as methotrexate, azathioprine, mycophenolate (at the exception of corticosteroid)
* Have received etanercept, infliximab, certolizumab, adalimumab, golimumab, or anakinra within 12 weeks of screening; tocilizumab, abatacept, ustekinumab, rituximab, belimumab, or any other B cell targeted therapies (approved or investigational) within 24 weeks of screening; or any other biologic therapy within 4 weeks of inclusion, whichever is longer.
* ASAT \> 5 times upper fold of the normal or ALAT \> 5 times upper fold of the normal or total bilirubin \> upper 1.5 fold of the normal
* hepatic impairment defined by Child Pugh B or C
* Have evidence of active tuberculosis as documented by medical history, clinical symptoms, and abnormal chest x-ray at screening together with positive quantiferon or T spot test or positive culture
* Have evidence of latent TB (as documented by a positive quantiferon or T spot test, no clinical symptoms consistent with active TB, and a normal chest x-ray at screening, or as outlined below) unless patient completes at least 4 weeks of appropriate treatment prior to inclusion and agrees to complete the remainder of treatment while in the trial.
* Renal impairment with estimated creatinine clearance \< 50 ml/mn (Cockroft and Gault formula)
* Have had any major surgery within 8 weeks prior to screening or will require major
* surgery during the study that, in the opinion of the investigator in consultation with the principal investigator, would pose an unacceptable risk to the patient.
* Past history of lymphoproliferative disease
* Past history of acute myocardial infection or unstable angina
* Past history of stroke (including transient ischemic attack)
* Uncontrolled hypertension defined as sustained blood pressure (BP) \> 150 mm Hg systolic BP (SBP), or \> 100 mm Hg diastolic BP (DBP) despite optimal antihypertensive treatment
* Past history NYHA (New York Heart Association) class III or IV congestive heart failure
* Thromboembolic event within 6 months before inclusion
* current or past long-time smokers defined by more than 15 pack years
* Second or third atrioventricular block
* Active cancer
* Past history of cancer the 5 years before the inclusion with the following exception:
* -Patients with cervical carcinoma in situ that has been resected with no evidence of recurrence or metastatic disease for at least 3 years may participate in the study.
* -Patients with basal cell or squamous epithelial skin cancers that have been completely resected with no evidence of recurrence for at least 3 years may participate in the study.
* Have had symptomatic herpes zoster infection within 6 months prior to screening
* Have a past history of recurrent symptomatic zona (one single symptomatic zona that had occurred more than 6 months before the inclusion is not a contra-indication)
* Have a history of disseminated/complicated herpes zoster (for example, multidermatomal involvement, ophthalmic zoster, CNS involvement, or post-herpetic neuralgia).
* Have been exposed to a live vaccine within 12 weeks prior to planned inclusion or are expected to need/receive a live vaccine during the course of the study (with the exception of herpes zoster vaccination that must occur \> 4 weeks prior to inclusion).
* Have active or chronic viral infection from hepatitis B virus (HBV, defined by positive aghbs), hepatitis C virus (HCV, defined by positive PCR), or human immunodeficiency virus (HIV, defined by positive serology).
* Patients under guardianship (tutelle/curatelle)
* Patient deprived of liberty under judicial or administrative decision.
* Participation in another interventional trial
* Hypersensitivity to the active substance (baricitinib) or to any of the excipients
* Past history of organ transplantation
* Surgery of the target IHCA required at diagnosis validated by a multidisciplinary tumor board during the screening process due to the following reason:
* Male with HCA accessible to liver resection (male not accessible to surgery based on a multidisciplinary tumor board evaluation could be included)
* Activation of the Wnt/B-catenin pathway at immunohistochemistry (diffuse positive glutamine synthase and/or nuclear translation of B-catenin) or mutations in exon 3 of CTNNB1 at molecular biology (except in this tumor is considered as unresectable) at the pathological reviewing
* Signs of malignant transformation in HCC (suspected by multidisciplinary tumor board based on imaging features or results of histology)
* Any other reasons validated by the multidisciplinary tumor board
