  We use entanglement entropy signatures to establish non-Abelian topological
order in projected Chern-insulator wavefunctions. The simplest instance is
obtained by Gutzwiller projecting a filled band with Chern number C=2, whose
wavefunction may also be viewed as the square of the Slater determinant of a
band insulator. We demonstrate that this wavefunction is captured by the
$SU(2)_2$ Chern Simons theory coupled to fermions. This is established most
persuasively by calculating the modular S-matrix from the candidate ground
state wavefunctions, following a recent entanglement entropy based approach.
This directly demonstrates the peculiar non-Abelian braiding statistics of
Majorana fermion quasiparticles in this state. We also provide microscopic
evidence for the field theoretic generalization, that the Nth power of a Chern
number C Slater determinant realizes the topological order of the $SU(N)_C$
Chern Simons theory coupled to fermions, by studying the $SU(2)_3$ (Read-Rezayi
type state) and the $SU(3)_2$ wavefunctions. An advantage of our projected
Chern insulator wavefunctions is the relative ease with which physical
properties, such as entanglement entropy and modular S-matrix can be
numerically calculated using Monte Carlo techniques.
