  The gauge-mediated model of supersymmetry breaking implies that stable
non-topological solitons, Q-balls, could form in the early universe and
comprise the dark matter. It is shown that the inclusion of the effects from
gravity-mediation set an upper limit on the size of Q-balls. When in a dense
baryonic environment Q-balls grow until reaching this limiting size at which
point they fragment into two equal-sized Q-balls. This Q-splitting process will
rapidly destroy a neutron star that absorbs even one Q-ball. The new limits on
Q-ball dark matter require an ultralight gravitino m_3/2 < keV, naturally
avoiding the gravitino overclosure problem, and providing the MSSM with a dark
matter candidate where gravitino dark matter is not viable.
