Filtered deformations of commutative algebras of Krull dimension two

Let F be an algebraically closed field of positive characteristic and let R be a finitely generated F-algebra with a filtration with the property that the associated graded ring of R is a finitely generated integral domain of Krull dimension two. We show that under these conditions R satisfies a polynomial identity, answering a question of Etingof in the affirmative in a special case.