  The collapse of flexible polyelectrolytes in a solution of multivalent
counterions is studied by means of a two state model. The states correspond to
rod-like and spherically collapsed conformations respectively. We focus on the
very dilute monomer concentration regime where the collapse transition is found
to occur when the charge of the multivalent salt is comparable (but smaller) to
that of the monomers. The main contribution to the free energy of the collapsed
conformation is linear in the number of monomers $N$, since the internal state
of the collapsed polymer approaches that of an amorphous ionic solid. The free
energy of the rod-like state grows as $N\ln N$, due to the electrostatic energy
associated with that shape. We show that practically all multivalent
counterions added to the system are condensed into the polymer chain, even
before the collapse.
