Argentoliveingite, ideally Ag3+xPb36-2xAs51+xS112 (0 <= x < 0.5), is a new silver-bearing sulphosalt species found in the Lengenbach deposit, Binntal, Canton Wallis, Switzerland. Associated minerals in the holotype, an old museum specimen, are baumhauerite and argentobaumhauerite. In other samples, hendekasartorite, liveingite, rathite and dufrenoysite are present. Argentoliveingite is dark grey and opaque with metallic lustre and a black streak. It is brittle without any discernible cleavage and with conchoidal fracture. In reflected light argentoliveingite is white, pleochroism is not discernible. Red internal reflections are seen on thin edges or at grain boundaries. In crossed polarisers, anisotropism is moderate in dark grey - neutral rotation tints. The reflectance data [R-min, R-max (%), in air] are: 36.6, 41.5 at 470 nm, 34.4, 39.4 at 546 nm, 32.9, 37.8 at 589 nm and 30.7, 35.2 at 650 nm. Mohs hardness is four, microhardness VHN25 exhibits a range 208-225 kg mm(-2), with a mean value of 217 kg mm(-2). The average result of 22 electron-microprobe spot analyses for the structurally investigated grain is (in wt%): Ag 2.31(4), Tl 0.35(12), Pb 46.65(26), Sb 0.83(10), As 25.36(14), S 24.27(17), total 99.97(20), corresponding to Ag3.17Tl0.40Pb33.31Sb1.01As50.08S112.02 (on the basis of 88Me + 112S = 200 atoms per formula unit, apfu). The ideal formula is in accordance with the results of the crystal-structure analysis and may be derived from the double ideal liveingite formula, Pb40As48S112, by minor substitution of Sb for As, and the independent, heterovalent [(Ag,Tl)(+) + (As,Sb)(3+)] <-> 2Pb(2+) substitution. The density, 5.23 g cm(-3), was calculated using the empirical formula. Argentoliveingite is triclinic, space group P<(1)over bar> (no. 2), with a = 7.905(2), b = 8.469(2), c = 137.96(4) angstrom, alpha = 89.592(2), beta = 88.969(2), gamma = 89.893(2)degrees, V = 9235(5) angstrom(3) and Z = 2. The c axis is double the b axis of liveingite and represents the longest unit-cell parameter for a known natural sulphosalt. The strongest five lines in the (calculated) powder-diffraction pattern are [d in angstrom(I)(h,k,l)]: 3.781(85)((2) over bar ,0,10), 3.668(100)((1) over bar ,0,33), 3.553(83)(1,0,35), 3.009(91)((1) over bar ,2,27) and 2.938(94)(1,(2) over bar ,29). Argentoliveingite is a homeotype of liveingite and a new member of the sartorite homologous series with N = 3.67, and with a limited extent of the uncoupled substitutions of [Ag+ + As3+] for 2Pb(2+) and [Tl+ + As3+] for 2Pb(2+). In argentoliveingite the sequence of alternating N = 3 and N = 4 slabs is different from that in liveingite and is further modified by alternation of three, chemically distinct, types of N = 4 slabs. The length and arrangement of crankshaft chains of short As-S bonds differ between different slabs, and especially between the N = 4 slabs of liveingite and argentoliveingite. The crystal structures of liveingite and Ag-bearing liveingite (both quantitatively analysed) have been refined for comparison purposes. The uncertain relationship with the phase "rathite-IV" is discussed.