Polycrystalline samples of Ln(18)Li(8)Rh(5)O(39) (Ln = La, Pr) have been synthesized by the ceramic method and characterized by X-ray and neutron diffraction, The compounds crystallize in the cubic space group Pm3n, with a(0) approximate to 12.1 angstrom. The unit cell contains four intersecting < 111 > chains, each comprised of an alternating sequence of face-sharing RhO6 octahedra and LiO6 trigonal prisms. The octahedra located at the points of intersection contain Rh4+, whereas the remainder contain Rh3+; the compounds thus contain a charge-ordered arrangement of the two cations. The polyhedral chains are enclosed in tunnels formed by the Ln-O sublattice. The magnetic properties of the two new compounds are discussed briefly: both are paramagnetic over the temperature range 5 < T(K)< 300.