  We propose a feasible experimental scheme to realize a three-dimensional
chiral topological insulator with cold fermionic atoms in an optical lattice,
which is characterized by an integer topological invariant distinct from the
conventional $Z_2$ topological insulators and has a remarkable macroscopic
zero-energy flat band. To probe its property, we show that its characteristic
surface states---the Dirac cones---can be probed through time-of-flight imaging
or Bragg spectroscopy and the flat band can be detected via measurement of the
atomic density profile in a weak global trap. The realization of this novel
topological phase with a flat band in an optical lattice will provide a unique
experimental platform to study the interplay between interaction and topology
and open new avenues for application of topological states.
