Chalmers was born in Edinburgh, the son of a herald painter to the Lyon court. He worked as a heraldic painter and engraver, which influenced the linear quality of his work, as well as studying with Allan Ramsay. After spending time in Florence and Minorca in 1751, due to his Jacobite sympathies, Chalmers returned to Edinburgh around 1760. He became a successful portrait painter, producing his best works in the 1770s. Chalmers later lived in Hull before moving to London in 1784, where he spent the last years of his life.