Deformation of metals and alloys by dislocations gliding between well-separated slip planes is a well-understood process, but most crystal structures do not possess such simple geometric arrangements. Examples are the Laves phases, the most common class of intermetallic compounds and exist with ordered cubic, hexagonal, and rhombohedral structures. These compounds are usually brittle at low temperatures, and transformation from one structure to another is slow. On the basis of geometric and energetic considerations, a dislocation-based mechanism consisting of two shears in different directions on adjacent atomic planes has been used to explain both deformation and phase transformations in this class of materials. We report direct observations made by Z-contrast atomic resolution microscopy of stacking faults and dislocation cores in the Laves phase Cr2Hf. These results show that this complex dislocation scheme does indeed operate in this material. Knowledge gained of the dislocation core structure will enable improved understanding of deformation mechanisms and phase transformation kinetics in this and other complex structures.