What is paradoxical about Levinthal paradox?

We would be tempted to state that there has never been a Levinthal paradox. Indeed, Levinthal raised an interesting problem about protein folding, as he realized that proteins have no time to explore exhaustively their conformational space on the way to their native structure. He did not seem to find this paradoxical and immediately proposed a straightforward solution, which has essentially never been refuted.

In other words, Levinthal solved his own paradox.