Background info from Wikipedia & More:

Information about the two sequels to Pirates of the Caribbean: The Curse of the Black Pearl was revealed at a Disney Investor Conference Studio Presentation in 2005. The title for the first sequel Dead Man’s Chest was revealed, and a second sequel was promised for a summer 2007 theatrical release. Filming began on February 28, 2005, with locations once again in the Costa Alegre, in Jalisco (Mexico). The sequel also includes ... read more

location shooting in Dominica as well as The Bahamas. The filmmakers are largely shooting the two sequels back-to-back, à la The Matrix Reloaded and The Matrix Revolutions as well as Back to the Future Part II and Part III, although throughout 2005 Dead Man’s Chest was the main focus of attention, with a collection of scenes for the third movie being shot. Because of the back-to-back setup, filming Dead Man’s Chest did not finish until February 7th 2006 [2]. Although they were filmed back to back they are being released in the same fashion as The Lord of the Rings movie trilogy, one year apart, and filming for the third movie continues into 2006.

Dead Man’s Chest premiered at Disneyland in Anaheim, California on June 24, 2006. Two days prior to the the re-opening day of the refurbished Pirates of the Caribbean attraction on which the movie trilogy is based. The refurbished attraction will include an adjusted storyline and Audio-Animatronics based on the movies and will open June 26, 2006.