Chaos Mode is the hardest difficulty in God of War III and to unlock it, completion one of three easier difficulty settings is required. Completing Chaos Mode doesn't unlock any specialties unlike in the previous games.
In Chaos mode, the grunts and beast of Olympus are more savage and attack in more organised formations, while bosses also get a lot tougher. For example, Hades becomes incredibly challenging to defeat and even weak bosses and enemies become a challenge due to their increased ferocity. Kratos is slightly more vulnerable to attacks and therefore takes a lot more damage. The combination of both changes results in attacks that are almost lethal if not blocked or evaded.
This mode forces the player to be more creative and to use particular weapons more often. The Bow of Apollo is such a weapon, during both the Hades and the Zeus boss fights, it's almost indispensable which isn't the case in the lower difficulties.