Filmmaker Clint Eastwood\'s \"J. Edgar,\" starring Leonardo DiCaprio, will have its world premiere on the opening night of AFI Fest 2011 in Los Angeles. The American Film Institute announced its plans Tuesday to unveil the J. Edgar Hoover bio-picture at the film festival Nov. 3. Co-starring Naomi Watts, Armie Hammer and Judi Dench and written by Dustin Lance Black, the movie explores the public and private life of Hoover, founding director of the FBI. \"Clint Eastwood is an American icon -- one whose work as a director, actor, producer and composer not only stands the test of time, but also continues to add new, rich chapters with each passing year,\" Bob Gazzale, president and chief executive officer of the American Film Institute, said in a statement Wednesday. \"What a gift it is to be going to the movies when Clint Eastwood is making them, and what an honor it is for the American Film Institute to premiere his latest contribution to America\'s cultural legacy.\"