The compounds Cs6Ti6S27 and Cs4BaTi6Se27 have been synthesized by means of the reactive flux method. CS6-Ti6S27 and Cs4BaTi6Se27 crystallize in a new structure type in the trigonal space group C-3(4)-R3 with three formula units in cells with hexagonal axes at T = 153(2) K of a = 13.5203(8) Angstrom, c = 19.784(1) Angstrom and a = 13.804(2) Angstrom, c = 20.850(2) Angstrom, respectively. The compounds Rb5AgTi6Se27 and Cs5AgTi6Se27 have also been synthesized by the reactive flux method. Rb5AgTi6Se27 and Cs5AgTi6Se27 crystallize in the trigonal space group C-3 nu(4)-P31c With two formula units in cells with hexagonal axes at T = 153(2) K of a 13.266(1) Angstrom, c = 13.908(2) Angstrom and a = 13.5713(4) Angstrom, c = 13.9367(6) Angstrom, respectively. The polar structures are closely related and consist of similar infinite one-dimensional (1)(infinity)[Ti-2(Q(2))(4)(Q)(2-)] (Q = S, Se) chains that run along [001] and are separated by cations. If these chains are considered to be cylinders, then these structures adopt hexagonal closest-packing along [001], a general feature of the packing for known A/group IV/Q compounds (A = alkali metal). These chains are built from seven-coordinate TiQ(7) pentagonal bipyramids that are bonded together by edge- and face-sharing in turn. Four Q(2)(2-) groups are in the translational unit of the chain. An unusual feature of the Ag chalcogenides is octahedral coordination about Ag.