Infinitism, in contrast to foundationalism and coherentism, claims that justification in any proposition requires the availability of an infinite chain of propositional reasons, each providing a justificatory reason for its successor in the chain. Both infinitists and some critics of the theory have at times noted the possibility that the theory may have sceptical consequences for doxastic justification. It is argued here that, for reasons that appear not to have been previously appreciated, sceptical results very definitely do follow from infinitism. (...) On one construal of infinitism, this constitutes a reductio of the theory. On an alternative construal, infinitists may embrace the sceptical conclusion, but in doing so, will take on all the problems that scepticism faces. (shrink)