The Sistine Chapel is the famous chapel in the Vatican next to St. Peters. Michelangelo, the great Florentine painter, painted the whole ceiling of the chapel with Biblical themes.
It's also the place where they lock up the cardinals to elect a new Pope.
Also, the Sistine Chapel ceiling and the Mona Lisa are masterpieces - everyone who knows them can name the artist. So as well as saying that he's going to make her a thing of beauty he's saying that the work he does on her will make his own reputation - that she is an opportunity for him to show how good he is.