To act exactly as you are supposed to; behave properly; obey. That new teacher really makes the students walk the chalk. In some classes the students play and talk, but Mr. Parker makes them walk the chalk. That theater owner wants his place to be orderly, and if boys and girls don't walk the chalk, he puts them out. (From the fact that sailors used to be asked to walk a chalk line along the deck of the ship to prove they were not drunk.)
Compare: TOE THE MARK.