Is god of war chains of Olympus number 4

If you mean like it is the forth game then no its not for 2 reasons:

1. in god of war 3 wen you are looking for hades he tells you who u have killed so far between the gods, "His brother, Posiden, is niece, Athena, is nefew, Ares, and his wife Pereshpone" the last boss battle was with Pereshpone in God of War Chains of Olympus
2. in god of war 2 you have to go talk to atlas who is holding the world on his shoulders you put him there in god of war chains of olympus

If you are looking for the order of games it goes like this:

1. God of War: Chains of Olympus
2. God of War
3. God of War: Ghost of Sparta
4. God of War 2
5. God of War 3
6. And if they rumors are right God of War 4 (which supposily comes out in 2012

P.S. God of War: Chains of Olympus and Ghost of Sparta are prequels