We perform first-principles structure optimization, phonon frequency and finite temperature molecular dynamics calculations based on density functional theory to study the interaction of chlorine atoms with graphene predicting the existence of possible chlorinated graphene derivatives. The bonding of a single chlorine atom is ionic through the transfer of charge from graphene to chlorine adatom and induces negligible local distortion in the underlying planar graphene. Different from hydrogen and fluorine adatoms, the migration of a single chlorine adatom on the surface of perfect graphene takes place almost without barrier. However, the decoration of one surface of graphene with Cl adatoms leading to various conformations cannot sustain due to strong Cl-Cl interaction resulting in the desorption through the formation of Cl$_2$ molecules. On the contrary, the fully chlorinated graphene, chlorographene CCl, where single chlorine atoms are bonded alternatingly to each carbon atom from different sides of graphene with $sp^3$-type covalent bonds, is buckled. We found that this structure is stable and is a direct band gap semiconductor, whose band gap can be tuned by applied uniform strain. Calculated phonon dispersion relation and four Raman-active modes of chlorographene are discussed.
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