  We study the perturbative renormalizability of chiral two pion exchange for
the singlet and triplet channels within effective field theory, provided that
the one pion exchange piece of the interaction has been fully iterated. We
determine the number of counterterms/subtractions needed in order to obtain
finite results when the cut-off is removed, resulting in three counterterms for
the singlet channel and six for the triplet. The results show that chiral two
pion exchange can be treated perturbatively up to a center-of-mass momentum of
k ~ 200-300 MeV in the singlet channel and k ~ 300-400 in the triplet.
