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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 >10¹² Ω) 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.