We report the new layered chalcogenides A(x)Cd(x)Bi(4-x)Q(6) (A = Cs, Rb, K; Q = S and A = Cs; Q = Se). All compounds are isostructural crystallizing in the orthorhombic space group Cmcm, with a = 4.0216(8) angstrom, b = 6.9537(14) angstrom, c = 24.203(5) angstrom. for Cs1.43Cd1.43Bi2.57S6 (x = 1.43); a = 3.9968(8) angstrom, b = 6.9243(14) angstrom, c = 23.700(5) angstrom for Rb1.54Cd1.54Bi2.46S6 (x = 1.54); a = 3.9986(8) angstrom, b = 6.9200(14) angstrom, c = 23.184(5) angstrom for K1.83Cd1.83Bi2.17S6 (x = 1.83) and a = 4.1363(8) angstrom, b = 7.1476(14) angstrom, c = 25.047(5) angstrom for Cs1.13Cd1.13Bi2.87Se6 (x = 1.13). These structures are intercalated derivatives of the Bi2Se3 structure by way of replacing some Bi3+ atoms with divalent Cd2+ atoms forming negatively charged Bi2Se3-type quintuple [CdxBi2-xSe3](x-) layers. The bandgaps of these compounds are between 1.00 eV for Q = Se and 1.37 eV for Q = S. Electronic band structure calculations at the density functional theory (DFT) level indicate Cs1.13Cd1.43Bi2.87Se6 and Cs1.43Cd1.43Bi2.57S6 to be direct band gap semiconductors. Polycrystalline Cs1.43Cd1.43Bi2.57S6 samples show n-type conduction and an extremely low thermal conductivity of 0.33 W.m(-1).K-1 at 773 K. The cesium ions between the layers of Cs1.43Cd1.43Bi2.57S6 are mobile and can be topotactically exchanged with Pb2+, Zn2+, Co2+ and Cd2+ in aqueous solution. The intercalation of metal cations presents a direct "soft chemical" route to create new materials.