Enchanted creature has lifelink and "Whenever a creature an opponent controls dies, put a +1/+1 counter on this creature." (Damage dealt by a creature with lifelink also causes its controller to gain that much life.)
11/17/2017 Multiple instances of lifelink on the same creature are redundant.
11/17/2017 If the enchanted creature is dealt lethal damage at the same time as a creature an opponent controls, they’re destroyed at the same time. It won’t receive a +1/+1 counter from its ability in time to save it.