Finalizing an item to the chain does not pass Priority.
§ 337.1.a Core Rules PDF (officieel)
§ 337 Step 1: Finalize
§ 337.1 If there is at least one Chain Item Pending, the controller of the oldest Pending Chain Item must complete the steps of Playing that Pending Item until it is a Finalized Item or leaves the Chain. See rule 349. Playing Cards for more information on finalizing chain items.
