Norris' play, seen in early 2010 at Playwrights Horizons and at Washington D.C.'s Woolly Mammoth Theatre, focuses on a neighborhood's changing landscape over the course of five decades.
A production, directed by Rupert Goold, is currently playing at the West End's Wyndham's Theatre.
"I am deeply honored and totally flabbergasted to receive this recognition. I want to thank both Playwrights Horizons and Woolly Mammoth Theatre in D.C. for simultaneously taking a chance on this play, and to thank Steppenwolf Theatre in Chicago for their 10 years of support," said Norris in a statement.
The other finalists in the Drama category were John Guare's A Free Man of Color, which premiered earlier this season at Lincoln Center Theater, and Lisa D'Amour's Detroit, which premiered at Steppenwolf Theatre and which is scheduled to bow on Broadway this fall.
For more information and a complete list of winners and finalists, click here.