I suppose the postmodernists belong somewhere in the Counter-Enlightenment fold—although whether on the left or the right, philosophically, is difficult to say. ~Joseph Bottum
It is difficult, perhaps, because they aren’t Counter-Enlightenment people at all, but post-Enlightenment who have nothing in common with the Counter-Enlightenment except perhaps skepticism about the importance of the self and the power of reason.
There are important ways in which postmodernity is best understood as an extension of Enlightenment modernity rather than a rejection–undercutting the thrust of B.’s point–but there are certainly borad and readily observable parallels between C-E thought and postmodernism regarding the rejection of the autonomous/unitary/universal self.
As for suspicion of reason, I don’t know who exactly Bottum refers to here, but C-E hero Hamann’s views on language and reason also have interesting parallels in postmodern thought.