  Chiral symmetry provides the symmetry protection for a large class of
topological edge states. It exists in non-Hermitian systems as well, and the
same anti-commutation relation between the Hamiltonian and a linear chiral
operator, i.e., $\{H,\Pi\}=0$, now warrants a symmetric spectrum about the
origin of the complex energy plane. Here we show two general approaches to
identify and generate chiral symmetry in non-Hermitian systems, with an
emphasis on lattices with detuned on-site potentials that can vary in both
their real and imaginary parts. One approach utilizes the Clifford algebra
satisfied by the Dirac matrices, while the other relies on the simultaneous
satisfaction of non-Hermitian particle-hole symmetry and bosonic anti-linear
symmetry, extended beyond simple spatial transformations to include, for
example, an imaginary gauge transformation.
