We present a 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 x 10^6 Msun) galaxy with a faint optical counterpart at around 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.