Chacko is Ammu's brother, Mammachi's son, Rahel and Estha's uncle, and Sophie Mol's dad. He's one of those people we want to like but who can be really irritating. As a young man, Chacko got all the family's love and attention. He went on to be a Rhodes Scholar at Oxford University, which has made him a little full of himself. We can consider a number of the characters in the novel to be kind of elitist – Baby Kochamma, Mammachi, and Chacko are all people who seem to think they're better or more important than others – but Chacko is the only one with the credentials to back it up.
Chacko also occupies kind of a weird space in society. He's taken over the family's factory, Paradise Pickles and Preserves, so on one hand, we can see him as Mr. Big Boss Man. On the other hand, he calls himself a Marxist, which basically means that he believes that the workers of the world – the laboring class – should unite, rise up against the middle and upper classes, and fight for their rights. If this seems contradictory to you, you're not alone – the narrator tells us outright that Chacko's beliefs conflict with his actions.
When we think about who Chacko is on a personal level, it's important to look at his family life. When Chacko lived in England, he met and married Margaret Kochamma, a waitress at an Oxford café. She ultimately found him too lazy and slovenly and divorced him in favor of Joe, a more dependable biologist. Not only is Chacko heartbroken over Margaret, but he also has to deal with the fact that he will miss most of his daughter Sophie Mol's childhood. (Margaret asked Chacko to leave when Sophie Mol was just a baby.)
Chacko can't be a dad to Sophie Mol, but he can be a stand-in father figure for Estha and Rahel when they all find themselves living in Ayemenem together. Nevertheless, we get the vibe that Chacko feels like he's settling for what he can get, not for what he really wants. He is completely thrilled when Margaret and Sophie come to visit. It really seems like he wants to believe he can have them back in his life for good – which is perhaps one reason he refers to Margaret as his wife instead of as his ex. Chacko is someone we don't necessarily like all the time, but we can really feel for him. It's easy to see why he is the way he is.