With Cooper's involvement, the work has been bumped up from the previously announced one-night-only, free-of-charge staging on July 16.
Shanley is currently at the apex of his decades-long playwriting career. His work Doubt is the hit of the season, playing to crowds on Broadway. He has won the 2005 Pulitzer Prize for Drama and this year's Tony Award for Best Play.
The new drama is about "two officers who clash over an explosive incident." Shanley, who has directed his own work on occasion, will stage the piece. Doug Hughes directed the Off-Broadway and Broadway productions of Doubt.
Character actor Cooper won his Oscar in 2003 for "Adaptation." His other film credits include "Silver City," "American Beauty," "Lone Star," "Matewan," "The Horse Whisperer," "The Bourne Identity," "The Bourne Supremacy" and "City of Hope."