The formation of a ternary cerium germanide Ce4Rh4Ge3 was established. The crystal structure of this novel compound was determined by mean of single crystal and powder X-ray diffraction techniques to be of the monoclinic Nd4Rh4Ge3-type (space group C2/c, No.15, Pearson symbol mS44, Z = 4) with the lattice parameters: a = 21.027(6) Å, b = 5.7248(16) Å, c = 7.999(3) Å, β = 110.39(3) deg. The low-temperature physical properties of Ce4Rh4Ge3 were studied by means of magnetic susceptibility, magnetization, heat capacity, electrical resistivity and magnetoresistance measurements. The compound was found to order ferromagnetically at TC = 4.2(2) K. Its physical behavior in the paramagnetic state was found to be governed by interplay of crystalline electric field effect and Kondo interactions, with possible contribution due to valence fluctuations associated with one of the two inequivalent cerium atoms located in the crystallographic unit cell of Ce4Rh4Ge3.