A chemist was a scientist trained in the science of chemistry. Chemists studied the composition of matter and its small-scale properties such as density and acidity instead of large-scale properties like size and shape.
Arik Soong's mother was a chemist. (ENT: "Cold Station 12")
By 2151, Vulcan chemists had only ever managed to obtain small amounts of eisillium and thus were unable to study it in detail. (ENT: "Breaking the Ice")
Chemists stationed on the Janus VI colony were unable to analyze the corrosive agent responsible for the damage to their machinery. (TOS: "The Devil in the Dark")
During the mid-2360s, Vaatrik, a Bajoran chemist, ran the chemist's shop on Terok Nor. (DS9: "Necessary Evil")