  The infinite projected entangled simplex state (iPESS), a type of tensor
network (TN) state, has been used successfully for simulating and
characterizing {\it non-chiral} spin liquids on the kagome lattice. Here, we
demonstrate that iPESS also provides a faithful representation of a {\it
chiral} spin liquid (CSL) on the same lattice, namely the ground state of the
spin-$1/2$ kagome Heisenberg antiferromagnet with a scalar chirality. By
classifying local tensors according to SU$(2)$ and point group symmetries, we
construct a chiral ansatz breaking reflection $P$ and time reversal $T$
symmetries while preserving $PT$. The variational TN states are shown to host,
for bond dimension $D\ge 8$, a chiral gapless entanglement spectrum following
SU$(2)_1$ conformal field theory. The correlation function shows a small weight
long-range tail complying with the prediction of the TN bulk-edge
correspondence. %{\color{red}With more constraints included, the chiral ansatz
is reduced to a non-chiral one which preserves full point group symmetries due
to an emergent {\it tensor conservation law} and is of relevance to the ground
state at the Heisenberg point. Lastly, by simulations in the complete ansatz
family we discuss the transition from the non-chiral spin liquid to the CSL
induced by the scalar chirality term.} We identify a non-chiral manifold
spanned by only a subset of symmetric tensors where a new emergent {\it tensor
conservation law} is realized. This allows us to both probe the stability of
the non-chiral spin liquid and discuss its transition to CSL induced by a
scalar chirality term.
