Bogi got it right.
Any damage in excess of the cover rating done to a target behind cover continues on to hit the original target minus the damage (or Pen) absorbed by the cover.
example: space marine behind AP 4 cover gets shot at by single bolter round from chaos space marine. Let's say the damage is 15 points. Is the excess damage of 11 points negated and the AP protection drops to 3? Or do the 11 points go toward the space marine taking cover and the AP drops to 3?
In your example: Chaos Marine shot does 15 Pen 4 damage
Target, behind AP 4 cover, is hit in chest (10 armour, 8 TB)
The shot's AP is first applied to the cover, which tears right through it. Thus the cover doesn't lower the damage though it does negate all of the attacks Pen. The attack deals more damage than the cover's AP so the cover is reduced to 3 AP after resolving the attack.
15 damage Pen 0 continues onto the Space Marine. His armour negates 10 damage, leaving 5 left. The Space Marine's TB is more than enough to negate this remaining damage.
(Had the cover been AP 3 to begin with the damage going into the Space Marine would have been 15 damage Pen 1, and 14 Pen 0 if the cover's AP was 5.)