A stoichiometric derivative of graphene with a fluorine atom attached to each carbon is reported. Raman, optical, structural, micromechanical, and transport studies show that the material is qualitatively different from the known graphene-based nonstoichiometric derivatives. Fluorographene is a high-quality insulator (resistivity >1012Ω) with an optical gap of 3 eV. It inherits the mechanical strength of graphene, exhibiting a Young’s modulus of 100 N m−1 and sustaining strains of 15%. Fluorographene is inert and stable up to 400 °C even in air, similar to Teflon.