The discovery of novel materials with low thermal conductivity is paramount to improving the efficiency of thermoelectric devices. As lattice thermal conductivity is inversely linked to unit cell complexity, we set out to synthesize a highly complex crystalline material with glasslike thermal conductivity. Here we present the structure, transport properties, heat capacity, and magnetization of single-crystal Gd117Co56Sn112, a complex material with a primitive unit cell volume of similar to 6858 angstrom(3) and similar to 285 atoms per primitive unit cell (1140 atoms per face-centered cubic unit cell). The room temperature lattice thermal conductivity of this material is K-L, = 0.28 W/(m.K) and represents one of the lowest ever reported for a nonglassy or nonionically conducting bulk solid. Furthermore, this material exhibits low resistivity at room temperature, and thus represents a true physical system that approaches the ideal phonon glass-electron crystal.