  Custodial symmetries are common in the Standard Model of particle physics.
They arise when quantum corrections to a parameter are proportional to the
parameter itself. Here, we show that a custodial symmetry of the chiral type is
also present in a classical Su-Schrieffer-Heeger (SSH) electrical circuit with
memory (memcircuit). In the absence of memory, the SSH circuit supports a
symmetry-protected topological edge state. Memory induces nonlinearities that
break chiral symmetry explicitly and spreads the state across the circuit.
However, the resulting state is still protected against perturbations by the
ensuing custodial chiral symmetry. These predictions can be verified
experimentally and demonstrate the interplay between symmetry and memory.
