Because the car is being towed at a constant velocity, the car has a net acceleration of zero.  A free-body diagram with the car will have the weight of the car pulling down, the normal of the road pushing up, the tension of the rope pulling the car, and the frictional force pulling away.  

Since the car has no net force acting on it, the tension in the rope equals the frictional force opposing its motion.  Usually elementary physics courses assert that the frictional force is proportional to the normal force, but not equal the normal force.  This means that the tension in the chain does not equal the weight of the car.

The tension in the chain does not equal the weight of the car.  The statement is false.