God of War: Chains of Olympus is a prequel to the God of War series, which initially launched on the PlayStation 2 console in early 2005. This handheld precursor was not developed by the series' original makers at Santa Monica but rather Ready at Dawn Studios, who you might also recognize for another PSP effort in the Daxter spin-off.
For a handheld version of God of War, it's a good game. Though the story and controls are on the weaker end than the console counterparts, it stays true to the God of War series and gives you enough challenge/entertainment to enjoy. If you head to the PlayStation Store via your PSP, you'll be able to get a feel for the game with the demo first before you know for sure what you're in for.
Being an action-adventure title, you're playing as Kratos, the rageaholic of Greek mythology. He's been burned by many a foe over the years. A warrior with swords chained to his forearms, he swings his upgradable weapons around collecting colored orbs for health, experience points, and magic. Fighting off Minotaurs, harpies, and others whilst solving puzzles, this series has spawned six titles all together with a seventh now on the way.