The new mineral flaggite (IMA2021-044), Pb4Cu2+4Te6+2(SO4)2O11(OH)2(H2O), occurs at the Grand Central mine in the Tombstone district, Cochise County, Arizona, USA, in cavities in quartz matrix in association with alunite, backite, cerussite, jarosite and rodalquilarite. Flaggite crystals are lime-green to yellow-green tablets, up to 0.5 mm across. The mineral has a very pale green streak and adamantine lustre. It is brittle with irregular fracture and a Mohs hardness of ~3. It has one excellent cleavage on {010}. The calculated density is 6.137 g cm–3. Optically, the mineral is biaxial (+) with α = 1.95(1), β = 1.96(1), γ = 2.00(1) (white light); 2V = 54(2)°; pleochroism: X green, Y light yellow green, Z nearly colourless; X > Y > Z. The Raman spectrum exhibits bands consistent with TeO6 and SO4. Electron microprobe analysis provided the empirical formula Pb3.88Cu2+3.89Te6+2.08(SO4)2O11(OH)2(H2O) (–0.03 H). Flaggite is triclinic, P1, a = 9.5610(2), b = 9.9755(2), c = 10.4449(3) Å, α = 74.884(1), β = 89.994(1), γ = 78.219(1)°, V = 939.97(4) Å3 and Z = 2. The structure of flaggite (R1 = 0.0342 for 5936 I > 2σI) contains hexagonal-close-packed, stair-step-like layers comprising TeO6 octahedra and Jahn-Teller distorted CuO6 octahedra. The layers in the structure of flaggite are very similar to those in bairdite, timroseite and paratimroseite.