A model three-particle scattering situation consisting of a projectile incident on a target bound to a residual core was considered under the assumptions that there was a low-energy virtual state in the projectile-target channel, that the projectile and core did not interact, and that the projectile-target and target-core interactions were s-wave separable interactions. When the appropriate Faddeev equations were solved by inversion, an enhancement was found in the three-body elastic cross section for virtual state energies less than or comparable to the target-core binding energy. This enhancement was determined to be kinematical in origin.