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 CrCl₂ is an orthorhombic, quasi-one dimensional antiferromagnet (AFM) with (100) chains of CrCl₂ weakly bonded to neighboring chains. Ab initio electronic structure calculations show that an AFM configuration along the chain direction is the magnetic ground state, the second lowest state is ferromagnetic (FM), and the third lowest state consists of FM chains with AFM coupling to neighboring chains. Calculated phonon dispersions show that the structure is dynamically stable. The magnetic anisotropy energy (MAE) of 1.35 meV/u.c. favors cross-chain (001) alignment of the Néel vector as opposed to parallel chain alignment. Within the cross-chain direction, a smaller MAE of 0.76 meV/u.c. favors the (001) alignment over (010). Applying strain and electric field, we are able to control the Néel vector in thin films and 1D atomic wire structures. To elucidate the underlying mechanism of magnetic anisotropy, we analyze the spin-orbit coupling energy and orbital momentum of the Cr atoms.