  We construct a highly-symmetric periodic orbit of eight bodies in three
dimensions. In this orbit, each body collides with its three nearest neighbors
in a regular periodic fashion. Regularization of the collisions in the orbit is
achieved by an extension of the Levi-Civita method. Initial conditions for the
orbit are found numerically. Linear stability of the orbit is then shown using
a technique by Roberts. Evidence toward higher-order stability is presented as
an additional result of a numerical calculation.
