Animals with chitinous exoskeletons are insects. Chitin is a tough, flexible, and lightweight material that makes up the outer covering or exoskeleton of insects. The exoskeleton functions as a protective barrier, providing support and protection for the insect`s internal organs.

Option 2, sponges, do not have an exoskeleton made of chitin. Instead, they have a porous body structure made of cells and protein fibers called spongin.

Option 3, sea urchins, have a hard outer skeleton or test made of calcium carbonate, not chitin.

Option 4, snails, have a shell made of calcium carbonate, not chitin.

Therefore, the only correct option is option 1, insects, as they are the animals with a chitinous exoskeleton.