No they don't. An old fashioned chassis is just a frame to provide a vehicles stiffness and to provide anchorage and alignment for the various systems on the car.
Modern cars use a thing called unitary construction where the body shell itself provides its own stiffness and a chassis is not required. This kind of structure has the added advantage of allowing crumple zones to be incorporated into the shell making the car so much safer than one with a rigid chassis.
