The thermal conductivity к of the heavy-fermion superconductor CeIrIn5 was measured as a function of temperature down to Tc/8, for current directions perpendicular (J‖a) and parallel (J‖c) to the tetragonal c axis. For J‖a, a sizable residual linear term к0/T is observed, as previously, which confirms the presence of line nodes in the superconducting gap. For J‖c, on the other hand,к/T → 0 as T → 0. The resulting precipitous decline in the anisotropy ratio кc/кa at low temperature rules out a gap structure with line nodes running along the c-axis, such as the d-wave state favoured for CeCoIn5, and instead points to a hybrid gap of Eg symmetry. It therefore appears that two distinct superconducting states are realized in the CeMIn5 family.