The group of animals that is correctly matched with its characteristic feature without any exception is:

Option C: Chondrichthyes - possess cartilaginous endoskeleton.

Chondrichthyes are a class of fish that includes sharks, rays, and chimeras. They are characterized by their cartilaginous endoskeleton, which is made up of a tough, flexible tissue similar to the cartilage found in human ears and noses. Unlike other fish, they do not have bones in their skeletons.

Option A: Reptilia is incorrect because not all reptiles possess a 3-chambered heart with an incompletely divided ventricle. Some reptiles, such as crocodiles and alligators, have a 4-chambered heart that is similar to that of birds and mammals.

Option B: Chordata is incorrect because not all chordates possess a mouth with an upper and a lower jaw. Jawless fish, such as lampreys and hagfish, are also members of the chordate phylum.

Option D: Mammalia is incorrect because not all mammals give birth to live young. The platypus and echidna, both of which are mammals, lay eggs instead of giving birth to live young.

Therefore, the correct answer is Option C: Chondrichthyes - possess cartilaginous endoskeleton.