The New York Musical Theatre Festival and the Chaplin Corporation are presenting a play about Chaplin called 'Behind the Limelight'. The six performances start September 19th and end September 30th. Actress, Brooke Sunny Moriber will play the part of Edna Purviance. This play premiered in the summer of 2005. I have not heard any news about it, so something of interest for fans in the New York area.
Update Sept 21th: Here is a review on this play from theatermania.com
Link to the BEHIND THE LIMELIGHT official website.
July 21, 2005 - Playbill article
Vassar article on Limelight
Also, someone sent a couple more reviews you can see in comments.
MORE INFORMATION: The lyrics to the Limelight theme 'Eternally' and more...
UPDATE: Because of a related internet question I will place a short answer here - Edna Purviance was never in Limelight. Check this link for more.