Spin-frustrated systems are one avenue for inducing macroscopic quantum states in materials. However, experimental realization of this goal has been difficult because of the lack of simple materials and, if available, the separation of the unusual magnetic properties arising from exotic magnetic states from behavior associated with chemical disorder, such as site mixing. Here we report the synthesis and magnetic properties of a new series of magnetically frustrated materials, MgxCu4-x(OH)(6)Cl-2. Because of the substantially different ligand-field chemistry of Mg2+ and Cu2+, site disorder within the kagome layers is minimized, as directly measured by X-ray diffraction. Our results reveal that many of the properties of these materials and related systems are not due to disorder of the magnetic lattice but rather reflect an unusual ground state.