A new compound, IrMnSi, has been synthesized, and its crystal structure and magnetic properties have been investigated by means of neutron powder diffraction, magnetization measurements, and first-principles theory. The crystal structure is found to be of the TiNiSi type ͑ordered Co 2 P, space group Pnma͒. The Mn-projected electronic states are situated at the Fermi level, giving rise to metallic binding, whereas a certain degree of covalent character is observed for the chemical bond between the Ir and Si atoms. A cycloidal, i.e., noncollinear, magnetic structure was observed below 460 K, with the propagation vector q = ͓0,0,0.4530͑5͔͒ at 10 K. The magnetism is dominated by large moments on the Mn sites, 3.8 B / atom from neutron diffraction. First-principles theory reproduces the propagation vector of the experimental magnetic structure as well as the angles between the Mn moments. The calculations further result in a magnetic moment of 3.2 B for the Mn atoms, whereas the Ir and Si moments are negligible, in agreement with observations. A calculation that more directly incorporates electron-electron interactions improves the agreement between the theoretical and experimental magnetic moments. A band mechanism is suggested to explain the observed magnetic order.