The alkali metal/group 4 metal/polychalcogenides Cs4Ti3Se13, Rb4Ti3S14, Cs4Ti3S14, Rb4Hf3S14, Rb4Zr3Se14, Cs-4-Zr3Se14, and Cs4Hf3Se14 have been synthesized by means of the reactive flux method at 823 or 873 K. Cs4Ti3Se13 crystallizes in a new structure type in space group Cr-2(2)-P2(1) with eight formula units in a monoclinic cell at T = 153 K of dimensions a = 10.2524(6) Angstrom, b = 32.468(2) Angstrom, c = 14.6747(8) Angstrom, beta = 100.008(1)degrees. Cs4Ti3Se13 is composed of four independent one-dimensional (1)(infinity)[Ti3Se134-] chains separated by Cs+ cations. These chains adopt hexagonal closest packing along the [100] direction. The (1)(infinity)[Ti3Se134-] chains are built from the face- and edge sharing of pentagonal pyramids and pentagonal bipyramids. Formal oxidation states cannot be assigned in Cs-4-Ti3Se13. The compounds Rb4Ti3S14. Cs4Ti3S14, Rb4Hf3S14. Rb4Zr3Se14, Cs4Zr3Se14, and Cs4Hf3Se14 crystallize in the K4Ti3S14 structure type with four formula units in space group C-2h(6)-C2/C Of the monoclinic system at T = 153 K in cells of dimensions a = 21.085(1) Angstrom, b = 8.1169(5) Angstrom, c = 13.1992(8) Angstrom, beta = 112.835(1)degrees for Rb4Ti3S14; 21.329(3) Angstrom, b = 8.415(1) Angstrom, c = 13.678(2) Angstrom, beta = 113.801(2)degrees for Cs4Ti3S14; a = 21.643(2) Angstrom, b = 8.1848(8) Angstrom, c = 13.331(1) Angstrom, beta = 111.762(2)degrees for Rb4Hf3S14; a = 22.605(7) Angstrom, b = 8.552(3) Angstrom, c = 13.880(4) Angstrom, beta = 110.919(9)degrees for Rb4Zr3Se14; a = 22.826(5) Angstrom; b = 8.841(2) Angstrom. c = 14.278(3) Angstrom, beta = 111.456(4)degrees for Cs4Zr3Se14; and a = 22.758(5) Angstrom, b = 8.844(2) Angstrom, c = 14.276(3) Angstrom, beta = 111.88(3)degrees fur Cs4Hf3Se14. These A(4)M(3)Q(14) compounds (A = alkali metal; M = group 4 metal; Q = chalcogen) contain hexagonally closest-packed (1)(infinity)[M(3)Q(14)(4-)] chains that run in the [101] direction and are separated by A(+) cations. Each (1)(infinity)[M(3)Q(14)(4-)] chain is built from a [M(3)Q(14)] unit that consists of two MQ(7) pentagonal bipyramids or one distorted MQ(8) bicapped octahedron bonded together by edge- or face-sharing. Each [M(3)Q(14)] unit contains six Q(2)(2-) dimers. with Q-Q distances in the normal single-bond range 2.0616(9)-2.095(2) Angstrom for S-S and 2.367(1)-2.391(2) Angstrom for Se-Se. The A(4)M(3)Q(14) compounds can be formulated as (A(+))(4)(M4+)(3)(Q(2)(2-))(6)(Q(2-))(2).