From : http://gta.wikia.com/Parachute
"Parachutes are introduced in The Ballad of Gay Tony with a vastly improved design, flapping realistically with the wind when deployed. Parachutes are first used in the mission High Dive and then adopted for a number of missions in the game, and serves as an integral component for the game's interpretation of base jumps, which are available in single player mode as well as the multiplayer "Free Mode" (using the parachute in Team Deathmatch could allow for an entire team to paradrop into a combat zone). Base jumping in the game involves the player jumping off a number of skyscrapers in Liberty City onto moving trucks. After completing all of the jumps in single player, the parachute will appear in the player's safehouse."
Parachute Glitch Video Clip