 The project is based on an approach never tested in a randomized controlled trial in severe alcoholic hepatitis, targeting the group of patients at high risk of death 25-35 at 2 months. This approach is based on animal and human studies.Antibiotics are effective in animal models and in other circumstances characterized by liver failure such as gastrointestinal bleeding related to portal hypertension. The interest of studying this population is emphasized by the frequency of infections in these critically ill patients. Antibiotics will be administered before the development of any infection, as it is likely that these patients present with mesenteric bacterial adenitis without systemic signs of infection. Primary endpoint will be 2-month survival as most deaths occur within 60 days and treatment is given for 30 days. 