Because of its unique physical properties, graphene, a 2D honeycomb arrangement of carbon atoms, has attracted tremendous attention. Silicene, the graphene equivalent for silicon, could follow this trend, opening new perspectives for applications, especially due to its compatibility with Si-based electronics. Silicene has been theoretically predicted as a buckled honeycomb arrangement of Si atoms and having an electronic dispersion resembling that of relativistic Dirac fermions. Here we provide compelling evidence, from both structural and electronic properties, for the synthesis of epitaxial silicene sheets on a silver (111) substrate, through the combination of scanning tunneling microscopy and angular-resolved photoemission spectroscopy in conjunction with calculations based on density functional theory.