The new mineral theuerdankite, ideally Ag3AsO4, was found in the Alter Theuerdank Mine, Beerberg, St. Andreasberg, Goslar District, Lower Saxony, Germany. Theuerdankite occurs as aggregates of anhedral grains up to 3 mm in size, growing in cavities of strongly supergene-weathered material consisting of native silver and chlorargyrite (but with calcite present). It is dark violet, changing to reddish and black when exposed to the air and light. It has a grey to violet grey streak; when readily fresh, its streak is brownish-red. The Mohs hardness is ~2. It is brittle with no observable cleavage or parting and with a conchoidal fracture. The calculated density is 6.620 g⋅cm–3. In reflected light, theuerdankite is dark grey with a pinkish tint, with no observable bireflectance, pleochroism, or anisotropy. It shows dark red internal reflections. The reflectance values for wavelengths recommended by the Commission on Ore Mineralogy of the International Mineralogical Association are (R, %): 13.3 (470 nm), 12.8 (546 nm), 12.7 (589 nm) and 12.5 (650 nm). The empirical formula (based on 4 apfu) is Ag3.00As1.00O4. Theuerdankite is cubic, space group P$\bar{4}$3n, a = 6.144(2) Å, V = 231.93(13) Å3 and Z = 2. The six strongest powder X-ray diffraction lines are [dobs in Å, (I) hkl]: 3.0736, (22) 200; 2.7502, (100) 210; 2.5106, (55) 211; 1.7050, (36) 320; 1.6249, (44) 321; and 1.3412, (17) 421. The crystal structure of theuerdankite (R1 = 1.69% for 519 reflections having I > 3σ(I)), is isotypic to those of synthetic Ag3AsO4 and Ag3PO4. The Gram–Charlier development describing the higher-order tensors representing the atomic displacement parameters of the silver atom was implemented, documenting that silver tends to behave anharmonically in the theuerdankite structure at room temperature.