The structure of Cs-III, stable between 4.2 and 4.3 GPa at room temperature, has been determined from single-crystal x-ray diffraction data. Rather than the simple fcc structure previously reported [Hall et al., Science 146, 1297 (1964)], the data yield a complex new type of elemental structure which is orthorhombic (space group C222(1)) with 84 atoms in the unit cell. No evidence could be found for the fcc form reported previously, even in a further experiment, conducted under conditions close to those used by Hall et al., which also yielded the 84-atom structure.