We describe the crystal structure and elementary magnetic properties of a previously unreported ternary intermetallic compound, Cr4PtGa17, which crystallizes in a rhombohedral unit cell in the noncentrosymmetric space group R3m. The crystal structure is closely related to those of XYZ half-Heusler compounds, where X, Y and Z were reported to be single elements only, most straightforwardly illustrated by writing the formula as (PtGa2)(Cr4Ga14)Ga (X=PtGa2, Y = Cr4Ga14, Z = Ga). The magnetic Cr occupies a breathing pyrochlore lattice. Ferromagnetic ordering is found below TC ~61 K, by both neutron diffraction and magnetometer studies, with a small, saturated moment of ~0.25 B/Cr observed at 2 K, making Cr4PtGa17 the first ferromagnetically ordered material with a breathing pyrochlore lattice. A magnetoresistance of ~140% was observed at 2 K. DFT calculations suggest that the material has a nearly-half-metallic electronic structure. The new material, Cr4PtGa17, the first realization in possessing both half-Heusler-type structure and breathing pyrochlore lattice, might pave a new way to achieve novel types of half-Heusler compounds with breathing pyrochlore lattice.