Chobham armour does provide some protection against HEAT and HESH rounds . However , against APFSDS rounds it provides no protection at all . And as we all know that against tanks placement of shots is more important than what is shot. It's not a coincidence that IED's ( mostly artillery shells ) blew up Abraham tanks in Iraq.
APFSDS rounds are solid projectiles which by its nature would be far less affected by all the layers than the plasma jet of HEAT or the concussion of HESH. The projectile is a long thin pencil of some extremely hard and dense metal, with little fins on the back and a sharpened point. Where older tank rounds relied primarily on the power of the explosives they carried, a sabot round is entirely dependent on the muzzle velocity of the gun which fires it. The faster it's traveling, the harder it hits and the more it can penetrate. Chobham pales into insignificance.
The reason why tank guns are almost by definition smoothbore these days is the development of the APFSDS rounds. The Soviets realized it long ago that smoothbore guns were better for sabot rounds and therefore placed such a gun on the T 72 . At that time Chobham armour did not even exist . But then, there is something on earth called foresight.