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We report the synthesis and evidence of graphene fluoride, a two-dimensional wide bandgap semiconductor derived from graphene. Graphene fluoride exhibits hexagonal crystalline order and strongly insulating behavior with resistance exceeding 10 G Ω at room temperature. Electron transport in graphene fluoride is well described by variable range hopping in two dimensions due to the presence of localized states in the band gap. Graphene obtained through the reduction of graphene fluoride is highly conductive, exhibiting a resistivity of less than 100 k Ω at room temperature. Our approach provides a pathway to reversibly engineer the band structure and conductivity of graphene for electronic and optical applications.