The crystal structure of argentobaumhauerite is reported for the first time from a sulfosalt aggregate from Lengenbach deposit, Binntal, Switzerland. The chemical formula of argentobaumhauerite, calculated in agreement with the results of structure determination is Cu0.06Ag1.20Tl0.18Pb21.46Sb0.56As32.28S72.26. The difference from the idealized baumahuerite formula, Pb12As16S36, and from the formula of Ag-, Tl- and Sb-free baumhauerite from Moosegg, Austria, Pb11.80As16.28S35.92, expresses the Ag + As and Tl + As substitution for 2Pb. Argentobaumhauerite is triclinic, a = 7.9053(10), b = 8.4680(10), c = 44.4102(53) Å, α = 84.614(2), β = 86.469(2), γ = 89.810(2)°. V(cell) = 2954.16 Å3, space group P. Baumhauerite Pb11.80As16.28S35.92 from Moosegg is triclinic, a = 7.884(4), b = 8.345(4), c = 22.811(11) Å, α = 90.069(8), β = 97.255(8), γ = 90.082(8)°, V(cell) = 1488.8(13) Å3, space group P1. Both minerals represent the N1,2 = 3;4 = 3.5 member of the sartorite homologous series, with As-rich slabs separated by zigzag layers of trigonal coordination prisms of lead. In argentobaumhauerite the sequence of alternating N = 3 and N = 4 slabs of baumhauerite is further modified by alternation of two distinct types of N = 4 slabs, those with Pb present in the slab interior and those with the interior Pb substituted by Ag + As. The length and arrangement of crankshaft chains of short As–S bonds differs between different slabs, and especially between the N = 4 slabs of baumhauerite and argentobaumhauerite. The name ‘argentobaumhauerite’ replaces the preliminary name ‘baumhauerite-2a’ (IMA-CNMNC; accepted proposal 15-F).