Go to an inconspicuous part of the room such as a corner near the floor or near the ceiling.
Place a 1/4-sized measuring cup on the wall or ceiling and hold it there with your pointer and middle fingers. Place it so that the bottom of the cup is in contact with the wall.
Cut around the base of the measuring cup with the utility knife. Do this ever so gently to only cut through the paint layer and not the paper layer of the drywall.
Remove the measuring cup from the wall.
Insert the tip of the utility knife's razor blade into the one side of the precut circle and peel the paint chip up. Work it like this until there is enough of the paint chip to grab with your fingers.
Grab the peeling paint chip edge and peel it away from the wall or ceiling.