Operator Algebras with Unique Preduals We show that every free semigroup algebra has a (strongly) unique Banach space predual. We also provide a new simpler proof that a weak-$*$ closed unital operator algebra containing a weak-$*$ dense subalgebra of compact operators has a unique Banach space predual. Keywords:unique predual, free semigroup algebra, CSL algebraCategories:47L50, 46B04, 47L35