Aiolosite, ideally Na4Bi(SO4)3Cl, or better Na2(Na2Bi)(SO4)3Cl, is a new sulfate mineral isotypic to apatite. It was found in an active medium-temperature intracrater fumarole at La Fossa crater, Vulcano Island, Aeolian archipelago, Sicily, Italy. It occurs as acicular to slender prismatic crystals up to 0.5 mm long in an altered pyroclastic breccia, together with alunite, anhydrite, demicheleite-(Br), demicheleite-(Cl), bismuthinite, and panichiite. The symmetry is hexagonal (class 6/m), space group P63/m, with a = 9.626(3), c = 6.880(3) Å, V = 552.1(3) Å3, Z = 2. The habit is prismatic, terminated by the pinacoid or, more rarely, by a bipyramid. Aiolosite is colorless to white, with white streak; the luster vitreous. It is non-fluorescent. The calculated density is 3.589 g/cm3. The mineral is nonpleochroic, uniaxial (+), nω = 1.59(1), nε = 1.60(1), mean nobs = 1.593 (589 nm), ncalc = 1.620. The chemical analysis gave Na2O 20.65, K2O 0.96, Bi2O3 32.49, SO3 41.27, Cl 4.02, Br 0.75, (H2O 0.57 from structure refinement), –O = (Cl + Br) 0.98 wt%, total 99.73, corresponding to the empirical formula calculated on the basis of 13 anions: Na2(Na1.95K0.12Bi0.833+)∑2.90S3.06O12.08[Cl0.67Br0.06(H2O)0.19]∑0.92. The crystal structure has been refined to a final R index of 0.048. One of the two independent Ca sites of apatite is exclusively occupied by Na, and the other one by statistically distributed Na and Bi. The SO42− anion replaces the PO43− anion of apatite; the chloride anion is located in the partially occupied (s.o.f. = 0.81) position at x = 0, y = 0, z = 0. Whenever the chloride position is vacant, the position at x = 0, y = 0, z = 1/4 is occupied by water (s.o.f. = 0.19). The strongest 6 lines in the X-ray powder diffraction pattern [dobs (Å) (I) hkl] are: 2.853 (100) (121), 2.775 (85) (112), 3.432 (45) (002), 1.965 (35) (222), 2.306 (25) (310), 4.787 (20) (110). Both the mineral and the mineral name have been approved by the IMA CNMNC (No. 2008-015).