The propagation of Dyakonov–Tamm waves guided by the planar interface of an isotropic topological insulator and a structurally chiral material, both assumed to be nonmagnetic, was investigated by numerically solving the associated canonical boundary-value problem. The topologically insulating surface states of the topological insulator were quantitated via a surface admittance , which significantly affects the phase speeds and the spatial profiles of the Dyakonov–Tamm waves. Most significantly, it is possible that a Dyakonov–Tamm wave propagates co-parallel to a vector in the interface plane, but no Dyakonov–Tamm wave propagates anti-parallel to . The left/right asymmetry, which vanishes for , is highly attractive for one-way on-chip optical communication.