A new mineral, chladniite, Na2CaMg7(PO4)6, occurs as a single grain within a silicate-bearing inclusion in the Carlton (IIICD) iron meteorite. It is hexagonal, R3, a = 14.967, c = 42.595 Å. It is named for E.F.F. Chladni (1756–1827), who is widely regarded as the founder of the science of meteoritics. Chladniite is colorless and transparent when powdered. In polished section, the mineral is gray, dark, weakly bireflecting, and weakly anisotropic. Cleavage, rarely visible, is rhomboidal in plan. Polishing hardness is less than low-calcium orthopyroxene, but greater than Fe,Ni metal. Reflectance measurements at 589 nm give R1 = 5.3%, R2 = 5.6%. Assuming an absorption coefficient k = 0, the calculated refractive indices are n1 = 1.60, n2 = 1.62. Stronger reflections on Gandolfi X-ray film of chladniite are d = 3.694(0,1,11; 306)s, 3.558(0,2,10;0,0,12)m, 2.960(0,1,14)s, 2.753(1,3,10)s, 2.500(3,3,0)m, 2.126(2,4,10; 2,3,14; 0,2,19)m, and 1.851(701; 1,5,14; 6,0,12)m. Microprobe analysis gives, in weight percent, Na2O 6.57, CaO 6.59, MgO 33.5, FeO 2.23, MnO 0.30, SiO2 0.59, P2O5 49.9, total 99.68, leading to the empirical formula Na1.77Ca0.98Si0.08(Mg6.96Fe0.26Mn0.04)Σ=7.26(P0.98O4)6. Chladniite is the Mg analogue of fillowite and johnsomervilleite, which are Mn- and Fe-dominated end-members, respectively. Chladniite occurs with chlorapatite, olivine, orthopyroxene, plegioclase, schreibersite, Fe, Ni metal, and troilite.