A Layered two-anion compounds are of interest for their diverse electronic properties. The modular nature of their layered structures offers opportunities for the construction of complex stackings used to introduce or tune functionality, but the accessible layer combinations are limited by the crystal chemistries of the available anions. We present a layered three-anion material, Bi4O4Cu1.7Se2.7Cl0.3, which adopts a new structure type composed of alternately stacked BiOCuSe and Bi2O2Se-like units. This structure is accessed, by inclusion of three chemically distinct anions, which are accommodated by aliovalently substituted Bi2O2Se0.7Cl0.3 blocks coupled to Cu-deficient Bi2O2Cu1.7Se2 blocks, producing a formal charge modulation along the stacking direction. The hypothetical parent phase Bi4O4Cu2Se3 is unstable with respect to its charge-neutral stoichiometric building blocks. The complex layer stacking confers excellent thermal properties upon Bi4O4Cu1.7Se2.7Cl0.3: a room-temperature thermal conductivity (kappa) of 0.4(1) W/mK was measured on a pellet with preferred crystallite orientation along the stacking axis, with perpendicular measurement indicating it is also highly anisotropic. This k value lies in the ultralow regime and is smaller than those of both BiOCuSe and Bi2O2Se Bi4O4Cu1.7Se2.7Cl0.3 behaves like a charge-balanced semiconductor with a narrow band gap. The chemical diversity offered by the additional anion allows the integration of two common structural units in a single phase by the simultaneous and coupled creation of charge-balancing defects in each of the units.