The new compounds TlHg(6)Q(4)Br(5) (Q = S, Se) are reported along with their syntheses, crystal structures, and thermal and optical properties, as well as electronic band structure calculations. Both compounds crystallize in the tetragonal I4/m space group with a = 14.145(1) angstrom, c = 8.803(1) angstrom, and d(calc) = 7.299 g/cm(3) for TlHg6S4Br5 (compound 1) and a = 14.518(2) angstrom, c = 8.782(1) angstrom, and d(calc) = 7.619 g/cm(3) for TlHg6Se4Br5 (compound 2). They consist of cuboid Hg(12)Q(3) building units interconnected by trigonal pyramids of BrHg3, forming a three-dimensional structure. The interstitial spaces are filled with thallium and bromide ions. Compounds 1 and 2 melt incongruently and show band gaps of 3.03 and 2.80 eV, respectively, which agree well with the calculated ones. First-principles electronic structure calculations at the density functional theory level reveal that both compounds have indirect band gaps, but there also exist direct transitions at energies similar to the indirect gaps.