Despite a three-dimensional arrangement of its CuCl42- ions, the magnetic properties Of Cs2CuCl4 are explained by a two-dimensional frustrated triangular antiferromagnetic spin-lattice. The origin of this low-dimensional magnetism was explored by evaluating the spin exchange interactions of A(2)CuCl(4) (A = Cs, Rb, K, Na) on the basis of first principles density functional calculations. The calculated spin exchange parameters agree with experiment only when the Cs+ ions located between the CuCl42- ions are not neglected. The antiferromagnetic spin exchange interaction between adjacent CuCl42-ions is strongly reduced by the 6p orbitals of the intervening Cs+ ions when the arrangement of the CuCl42- and Cs+ ions has either mirror-plane or inversion symmetry. The observed magnetism Of Cs2CuCl4 arises from this symmetry-dependent participation of the 6p orbitals of the Cs+ ions in the spin exchange interactions between CuCl42- ions.