Option 1: Amphibia - Amphibians, like frogs and salamanders, do not have an exoskeleton. Instead, they have a soft and moist skin.

Option 2: Mammalia - Mammals, including humans, do not have an exoskeleton. They have an internal skeleton made of bones.

Option 3: Aves - Birds also do not have an exoskeleton. They have a lightweight skeleton made of bones.

Option 4: Chondrichthyes - This is the correct option. Chondrichthyes, which includes sharks and rays, do not have an exoskeleton. They have a cartilaginous skeleton, which is made of cartilage rather than bone.

In conclusion, the correct option is option 4, Chondrichthyes, as they are vertebrates that lack an exoskeleton.