  We study the nonspherical linear perturbations of the discretely self-similar
and spherically symmetric solution for a self-gravitating scalar field
discovered by Choptuik in the context of marginal gravitational collapse. We
find that all nonspherical perturbations decay. Therefore critical phenomena at
the threshold of gravitational collapse, originally found in spherical
symmetry, will extend to (at least slightly) nonspherical initial data.
