We present an HI synthesis imaging study of NGC 864 (CIG 96), a spiral galaxy well isolated from similarly sized companions, yet presenting an intriguing asymmetry in its integral HI spectrum. The asymmetry in the HI profile is associated with a strong kinematical perturbation in the gaseous envelope of the galaxy, where at one side the decay of the rotation curve is faster than Keplerian. We detect a small (M(HI) = 5 106 ) galaxy with a faint optical counterpart at ~80 kpc projected distance from NGC 864. This galaxy is probably not massive enough to have caused the perturbations in NGC 864. We discuss alternatives, such as the accretion of a gaseous companion at a radial velocity lower than the maximum.