Elastic neutron scattering experiments were carried out to investigate the magnetic structure and the critical behaviour of the mixed triangular antiferromagnetic system CsMn(Br 0.19 I 0.81 ) 3 , for which our previous magnetic measurement revealed the macroscopic anisotropy to be negligible. It is found that in the ordered state below T N = 8.29 K, the spin planes in which the spins lie with the 120 • structure are tilted from the basal plane, and that the average of the tilting angle φ is evaluated as cos 2 φ = 0.362, i.e. φ = 53 • . This result suggests that the present system is almost at the Heisenberg limit for the interaction. The critical exponent for the sublattice magnetization is obtained as β = 0.28 ± 0.02, which is in agreement with the value predicted for the chiral Heisenberg universality class.