CsCu3DyTe4 was prepared by reacting copper, dysprosium, and tellurium with cesium azide at 850 degrees C in a fused silica ampule. This new telluride crystallizes in the monoclinic space group C2/m with lattice dimensions of a = 16.462(4) angstrom, b = 4.434(1) angstrom, c = 8.881(2) angstrom, beta = 108.609(12)degrees with Z = 2. Its crystal structure is dominated by (2)(infinity){[Cu3DyTe4]}(1-) anionic layers separated by Cs+ cations. The copper cations are disordered over three different tetrahedral sites. The [DyTe6](9-) polyhedra form infinite (1)(infinity){[DyTe4](5-)} chains. Magnetism studies conducted on this semiconductor suggest complex magnetic interactions between the Dy3+ cations with a strong deviation from Curie-type behavior at low temperatures below 40 K.