Some of the primordial deities other than Chaos might oppose Percy. For instance, if there are deities who believe that Chaos has overstepped by raising a demigod in such an unorthodox way, they could send their minions or directly attack Percy. There could also be a group of rogue demigods who are jealous of Percy's connection to Chaos and his new - found powers, and they would try to undermine him at every turn.
The Titans could still be antagonists. Even though Percy is raised by Chaos, the Titans might see him as a threat to their plans of overthrowing the Olympians. They could try to capture or kill him to prevent him from interfering.
It could be some of the other trainees who are jealous of Percy's progress and his special relationship with Chaos.
The Titans could still be a major threat. Since Percy is now the Host of Chaos, they might see him as a new opportunity to regain power. Kronos could try to manipulate Percy's chaotic powers for his own gain, or maybe use Percy's new status to cause more chaos in the world and then step in to 'restore order' in a way that benefits the Titans.
The Titans could be great antagonists. They might see Percy as a threat to their plans of overthrowing the gods again. Since Percy has chaos powers, they could fear that he could disrupt their carefully laid - out schemes. Another possibility is some of the more traditional enemies of the demigods, like the monsters. They might be drawn to Percy's chaotic energy and try to either consume it or destroy him to prevent him from becoming too powerful.
Maybe the gods or powerful beings who are trying to maintain the current balance and see Percy's new role as a disruption. They would try to stop him from carrying out his assassinations in the chaos world.
The Titans could be great antagonists. Even though they were defeated once, they could be making a comeback with new strategies and powers, seeing the Chaos Army as a threat to their plans of regaining dominance. Another option could be the Giants, who are also powerful and have a long - standing grudge against the demigods.
A likely main antagonist could be a powerful demigod who has turned to the dark side and wants to use chaos for his own evil purposes. He might see Percy as a threat to his plans.
It could be the agents of Order who see Percy and Thalia joining Chaos as a threat to the balance they strive to maintain. They might send their best warriors to stop Percy and Thalia from carrying out Chaos' plans.
It could be the entities that thrive on the disorder in the chaos. They might see Percy and Bianca as threats to their way of life and try to stop them from achieving whatever goal they have in the chaos.
Some of the primordial gods who are jealous of Chaos's newfound relationship with Percy could be antagonists. They might view Percy as an upstart and try to undermine his position. For example, Erebus could try to create chaos in Percy's life in a more malicious way, not in the way that Chaos intends.
Obviously, Percy would be one of the main characters. Chaos, who raises him, would also be very important. There might also be some other primordial beings that interact with Percy during his upbringing.