While Chaos is a recurring antagonist in the Sonic series, his appearances are typically tied to the presence of the seven Chaos Emeralds. He is not known for reincarnation, unlike characters like Shadow the Hedgehog who has a more complex backstory.
In Sonic Adventure 2, Chaos is defeated by Sonic and his friends. His presence is felt in the story through the Shadow Androids, which are based on his form and created by Gerald Robotnik. However, Chaos himself does not return in the game.