Shakespeare in Original Pronunciation. (Reconstructed from phonetic spellings, period rhyme schemes, and other evidence.)
It doesn't sound like John Gielgud. (That familiar upper crust British accent emerged in the later 18th century.)
Be warned: it strikes the modern ear a bit oddly.
@LiberalLibrarian Okay, it sounds a bit strange as London standard and the dialect of Elizabeth's court, shall we say.