Well, to be fair, 'chink in the armor' and 'Achilles heel' do differ somewhat in connotation -- a chink in the armor connotes a (usually newly-found, usually repairable, often temporary) small weakness, whereas an Achilles heel connotes a small but inherent and (usually) permanent flaw that can be used in that person's/team's downfall -- c.f. kryptonite.