A new series of ternary rare-earth indium antimonides, (RE)In1-xSb2 (RE = La-Nd), has been synthesized through reaction of the elements at 950 degrees C. The structure of LaIn0.81(1)Sb-2 has been determined by single-crystal X-ray diffraction (monoclinic space group C-2(2h)-P2(1)/m, Z = 2, a = 4.521(3) Angstrom, b = 4.331(3) Angstrom, c = 11.913(7) Angstrom, beta = 99.6680(11)degrees). The structure is built up of alternating layers of compositions (2)(infinity)[Sb] and (2)(infinity)[In0.8Sb], separated by the La atoms. The (2)(infinity)[Sb] layer is described as a nearly square net of Sb atoms held by weak one-electron bonds, while the (2)(infinity)[In0.8Sb] layer is derived from edge-sharing InSb4 tetrahedra distorted in such a way as to produce In-In zigzag chains. Extended Huckel band structure calculations are used to explain the bonding and predict that anisotropic metallic behavior should be observed.