What was Shakespeare's first play?

We don't know, exactly. The first play we have any record of is Henry VI Part III referred to by Greene in 1592. This could be the "harey the vj" referred to in Henslowe's diary as having been premiered on March 3, 1591 by Lord Strange's Men. But it is also possible that Shakespeare had written even earlier plays which didn't go over so well or were not played by a company of which Henslowe took note.