Yes, chameleons are reptiles in general and lizards in particular. Jim's is a veiled chameleon like mine. These are "true" chameleons that not only can change color dramatically to match their mood or surroundings, they also have prehensile tails, long tongues they shoot out with lightning speed to catch prey and independently rotating eyes. A population of Jackson's chameleons (the ones with three horns like a triceratops) has been introduced into Hawaii; otherwise true chameleons only exist in the Old World, like Africa and Madagascar.
The little streamlined green or brown lizards we commonly call chameleons in the United States are technically anoles.