  We report the theoretical discovery of a systematic scheme to produce
topological flat bands (TFBs) with arbitrary Chern numbers. We find that
generically a multi-orbital high Chern number TFB model can be constructed by
considering multi-layer 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 inter-particle interactions, these
models are likely to lead to the formation of novel 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.
