Chemists recognize many different elements, such as gold, or oxygen, or carbon. Suppose you got some carbon, and started splitting it into smaller pieces. The smallest piece that would still be called "carbon" would be:

An Atom.

Explanation:

An atom is the smallest particle of a chemical element that can exist. It the fundamental piece of matter. Therefore, splitting carbon into smaller pieces, the smallest piece that would still be called "carbon" would be an Atom of carbon. However, atom is also made of three subatomic particles called electrons, protons and neutrons.