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, BiOCuSeCl, which adopts a new structure type composed of alternately stacked BiOCuSe and BiOSe-like units. This structure is accessed by inclusion of three chemically distinct anions, which are accommodated by aliovalently substituted BiOSeCl blocks coupled to Cu-deficient BiOCuSe blocks, producing a formal charge modulation along the stacking direction. The hypothetical parent phase BiOCuSe is unstable with respect to its charge-neutral stoichiometric building blocks. The complex layer stacking confers excellent thermal properties upon BiOCuSeCl: a room-temperature thermal conductivity (κ) 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 κ value lies in the ultralow regime and is smaller than those of both BiOCuSe and BiOSe. BiOCuSeCl 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.