The stability of the ion hybrid wave in a plasma containing two thermal ion species present in comparable proportions and a low density population of superthermal alpha-particles is analyzed. A simple, model distribution function consisting of a ring distribution in the perpendicular velocity and a Maxwellian in the parallel velocity is used for the superthermal alpha-particles. This distribution function is relevant to the core plasma of a tokamak in the immediate post-birth phase before the alpha-particles have had time to relax collisionally and is therefore of interest to the alpha-channelling question. It has also been used to interpret ion cyclotron emission from fusion products in the edge plasma of large tokamaks. An approximate dispersion relation is derived which allows the conditions for instability to be explored and an analytic expression for the growth rate to be obtained.