We report the theoretical discovery of a systematic scheme to produce topological flat bands (TFBs) with arbitrary Chern numbers. We find that generically a multiorbital high Chern number TFB model can be constructed by considering multilayer Chern number C = 1 TFB models with enhanced translational symmetry. A series of models are presented as examples, including a two-band model on a triangular lattice with a Chern number C = 3 and an N-band square lattice model with C = N for an arbitrary integer N. In all these models, the flatness ratio for the TFBs is larger than 30 and increases with increasing Chern number. In the presence of appropriate interparticle interactions, these models are likely to lead to the formation of Abelian and non-Abelian fractional Chern insulators. As a simple example, we test the C = 2 model with hardcore bosons at 1/3 filling, and an intriguing fractional quantum Hall state is observed. DOI: 10.1103/PhysRevB.86.241112