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 gTI, 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 u in the interface plane, but no Dyakonov–Tamm wave propagates anti-parallel to u. The left/right asymmetry, which vanishes for gTI = 0, is highly attractive for one-way on-chip optical communication