The Alchemist can be found in The Last Meal, in the main room.
You see a man in his forties. At first glance he seems to stare at you unfalteringly, but then you realize he has a glass eye. His face and hands are covered with burn-scars and unless you're mistaken, he's missing a couple of fingers on his left hand.
The alchemist offers a starter kit, which you can purchase for 50 gold. It contains: