Tennantite-(Cu), Cu12As4S13, was approved as a new mineral species from the Layo epithermal deposit, Castilla Province, Arequipa Department, Peru, where it occurs as black metallic anhedral grains, up to 0.1 mm across, replacing enargite and associated with chalcopyrite and vinciennite. In reflected light, tennantite-(Cu) is isotropic, grey with a bluish shade. Reflectance data for the four COM wavelengths in air are [λ (nm): R (%)]: 470: 29.1; 546: 28.4; 589: 27.4; and 650: 25.0. Electron microprobe analysis for holotype material gave (in wt.% – average of 10 spot analyses): Cu 49.32(27), Fe 2.20(12), Zn 0.09(2), Sn 0.03(5), As 19.45(43), Sb 1.94(10), Te 0.02(5), S 27.75(43), total 100.80(20). On the basis of (As + Sb + Te) = 4 atoms per formula unit (apfu), the empirical formula of tennantite-(Cu) is (Cu11.27Fe0.57Zn0.02)Σ11.86(As3.77Sb0.23)Σ4.00S12.57. Tennantite-(Cu) is cubic, I$\overline 4$3m, with unit-cell parameters a = 10.1710(10) Å, V = 1052.2(2) Å3 and Z = 2. Its crystal structure was refined by single-crystal X-ray diffraction data to a final R1 = 0.0178 on the basis of 263 unique reflections with Fo > 4σ(Fo) and 24 refined parameters. Tennantite-(Cu) is isotypic with other tetrahedrite-group minerals. Previous findings of tennantite-(Cu) are reported and some nomenclature issues, related to the Fe and Cu oxidation states, are discussed. At the Layo epithermal deposit, tennantite-(Cu) is the result of the replacement of enargite under decreasing $f_{{\rm S}_ 2}$ conditions.