I think this is Amnesia Moon by Jonathan Lethem.
The book reminds me a little of Philip K. Dick's approach to writing. It's set in a post nuclear war USA and it's a bit uncertain what is real and what isn't. There is a mysterious figure called Kellogg whose dreams change the world. The main protagonist is indeed called Chaos.
Chaos meets the girl covered in fur when he goes to the store in the local town Hatfork:
Chaos parked in the driveway and walked up to the main building. Cars littered the
grounds, some parked, some abandoned. The clouds had cleared, and the sun beat down now,
heating the pavement, making him feel his weakness. He heard voices inside and hurried
Sitting on the concrete steps between him and the lobby was a girl dressed in rags and
covered with fine, silky hair from head to foot. She squinted at Chaos as he approached. He smiled weakly and said, “Excuse me.” He felt dim with hunger
The reference to Playboy is when Chaos (aka Everett) starts arguing with a girl called Edie about whether people have transformed and become ugly or were always ugly. He goes to the mall to try and buy a Playboy to show Edie that women used to be beautiful. However it turns out you are only allowed to buy issues of Playboy with models whose body type matches yours. In Chaos' case because he is grossly fat he is only allowed to buy magazines with grossly fat models.
He found the shop, but the rack with the adult magazines was missing.
He asked the clerk, a normally proportioned man whose appearance was ruined by a
raspberry birthmark that covered most of his face like a splayed-out octopus. “We keep those behind the counter now,” the clerk explained. “What’ll it be—endomorph?”
“You know the new law, right?”
“New law? I just want to buy a copy of Playboy.”
“Fine. But the new law says you get the issue that corresponds to your body type. Midgets
look at midgets, and so on.” He swept his arm back, indicating the rack behind the cabinet.
Sure enough, there were ten or twelve different versions of Playboy, and the bodies Everett glimpsed on the covers were all distorted and wrong.
The clerk gave him the once-over. “Looks like endomorph to me,” he said. He flopped a
magazine onto the counter. The woman on the cover was leering and enormous.