It is shown that the guiding center motion around a single chain of magnetic islands in a sheared slab can become chaotic in the presence of a single prescribed low-frequency electrostatic wave. This process leads to radial diffusion across the islands without magnetic braiding. The chaotic diffusion appears to be selective in velocity space. Using realistic values of the physical parameters for a fusion plasma, it is concluded that this process can be effective in usual conditions: with the observed islands, and electronic field values corresponding to measured density fluctuations in the TFR Tokamak, this diffusion concerns ions with velocities higher than thermal, and almost all of the electron population. The consequences for radial diffusion are discussed.