He didn't meet Shakespeare in The Chase in fact, only watch Elizabeth I order him to write what becomes The Merry Wives of Windsor, and then be given the idea for Hamlet by Francis Bacon!

The Doctor has mentioned meeting Shakespeare before - in City of Death he claims to be able to authenticate the first draft of Hamlet because it's in his handwriting; but from Shakespeare's point of view The Shakespeare Code is their first meeting. Unless the Doctor has forgotten something and this is why Shakespeare knows that he's a time traveller...