Large free algebras in the ring of fractions of skew polynomial rings

It is shown that the division ring of quotients of a skew polynomial ring of automorphism type, if infinite-dimensional over its centre k and satisfying suitable hypotheses, contains the group algebra of a free group of large rank (usually at least \k\). The result applies, in particular, to the skew polynomial rings constructed from rational function fields, and affirmatively settles the conjectures of Makar-Limanov and Lichtman in this case.