  We investigate here the particle acceleration by naked singularities to
arbitrarily high center of mass energies. Recently it has been suggested that
black holes could be used as particle accelerators to probe the Planck scale
physics. We show that the naked singularities serve the same purpose and
probably would do better than their black hole counterparts. We focus on the
scenario of a self-similar gravitational collapse starting from a regular
initial data, leading to the formation of a globally naked singularity. It is
seen that when particles moving along timelike geodesics interact and collide
near the Cauchy horizon, the energy of collision in the center of mass frame
will be arbitrarily high, thus offering a window to Planck scale physics.
