  We consider a particle collision with a high center-of-mass energy near a
Ba\~nados-Teitelboim-Zanelli (BTZ) black hole. We obtain the center-of-mass
energy of two general colliding geodesic particles in the BTZ black hole
spacetime. We show that the center-of-mass energy of two ingoing particles can
be arbitrarily large on an event horizon if either of the two particles has a
critical angular momentum and the other has a non-critical angular momentum. We
also show that the motion of a particle with a subcritical angular momentum is
allowed near an extremal rotating BTZ black hole and that a center-of-mass
energy for a tail-on collision at a point can be arbitrarily large in a
critical angular momentum limit.
