Any time someone drinks a potion or rubs ointment on their armor chafing, Chemists are collecting money in the background. They channel all the cool magic White Mages and Healers can do into an ingestable form for the common folk, or put an Arcanist's poison clouds into a bomb for a Thief. Their concoctions are spread far and wide across the lands - all at a cost that the Chemist can pocket.
Chemists can't actually wield the magic of other classes, only 'grab' it and shove it in a bottle, so they rely on other people to do the work for them. Only initially though, as with a little input from the Chemist that one solution can be concentrated or diluted or have its effects manifest in a different way. In battle, they can chuck all sorts of damaging magic at enemies in the form of potions or bombs, as long as they are prepared beforehand. Many carry a small dagger in case they are caught off-guard.
Chemists are notorious for their cooking, perfumery and involvement in industrial processes - namely the clothes-dying industry. They are also chemists in the true sense of the word and have a keen sense for creating mixtures that revolutionise processes. For example, without Chemist input, the fur exported from Raan would be gross and unhygienic to wear, and nobody wants that. Business running also comes naturally to them, so where there's a Chemist, there's a Potion Seller.