The church turned once again to Caravaggio, asking him to complete a painting for the space. Caravaggio produced this work:
The church rejected this painting as well and if we take a closer look it is easy to understand why. The angel is guiding St. Matthew's hand which, combined with the look on his face, makes him look rather like a simpleton. In addition, the position of the Saint's dirty left foot puts it precariously close to the eucharist when it is raised during the liturgy. The painting eventually ended up in the Kaiser-Friedrich Museum in Berlin and was destroyed by American bombing in World War II.
Caravaggio, being the consummate professional that he was, painted a second version that remains in the chapel to this day:
For amazing hi-res images of the paintings in the Chapel visit: Contarelli Chapel hi-res pics.
And an interesting documentary on how they produced the above images: Caravaggio, creating three facsimiles.