Professor Chapman was an instructor at Starfleet Academy during the 2360s.

One of his students was B'Elanna Torres. Though Chapman and Torres fought constantly, he thought she was one of the finest students he ever taught and was sorry when she dropped out of the Academy. He placed a note in her permanent file saying he would support her re-entry if she ever re-applied. (VOY: "Parallax")

This character was only mentioned in dialogue.
The Starfleet Academy Handbook gives him the first name Paul.