  A system of three particles undergoing inelastic collisions in arbitrary
spatial dimensions is studied with the aim of establishing the domain of
``inelastic collapse''---an infinite number of collisions which take place in a
finite time. Analytic and simulation results show that for a sufficiently small
restitution coefficient, $0\leq r<7-4\sqrt{3}\approx 0.072$, collapse can
occur. In one dimension, such a collapse is stable against small perturbations
within this entire range. In higher dimensions, the collapse can be stable
against small variations of initial conditions, within a smaller $r$ range,
$0\leq r<9-4\sqrt{5}\approx 0.056$.
