  Doubts have been raised on the representation of chiral spin liquids
exhibiting topological order in terms of projected entangled pair states
(PEPSs). Here, starting from a simple spin-1/2 chiral frustrated Heisenberg
model, we show that a faithful representation of the chiral spin liquid phase
is in fact possible in terms of a generic PEPS upon variational optimization.
We find a perfectly chiral gapless edge mode and a rapid decay of correlation
functions at short distances consistent with a bulk gap, concomitant with a
gossamer long-range tail originating from a PEPS bulk-edge correspondence. For
increasing bond dimension, (i) the rapid decrease of spurious features -- SU(2)
symmetry breaking and long-range tails in correlations -- together with (ii) a
faster convergence of the ground state energy as compared to state-of-the-art
cylinder matrix-product state simulations involving far more variational
parameters, prove the fundamental relevance of the PEPS ansatz for simulating
systems with chiral topological order.
