  We perform an exact diagonalization study of the spin-$1/2$ XXZ Heisenberg
antiferromagnet on the kagome lattice at finite magnetization $m = \frac{2}{3}$
with an emphasis on the XY point ($J_z = 0$), and in the presence of a small
chiral term. Recent analytic work by Kumar, Sun and Fradkin [Phys. Rev. B 90,
174409 (2014)] on the same model, using a newly developed flux attachment
transformation, predicts a plateau at this value of the magnetization described
by a chiral spin liquid (CSL) with a spin Hall conductance of $\sigma_{xy} =
\frac{1}{2}$. Such a state is topological in nature, has a ground state
degeneracy and exhibits fractional excitations. We analyze the degeneracy
structure in the low energy manifold, identify the candidate topological states
and use them to compute the modular matrices and Chern numbers all of which
strongly agree with expected theoretical behavior for the $\sigma_{xy} =
\frac{1}{2}$ CSL. We argue that the evidence suggests the CSL is robust even in
the limit of zero external chirality.
