Pour about a cup of the chemical paint stripper into a wide-mouth metal can.
Brush a 3-foot-by-3-foot section of the fiberglass with the paint stripper. Allow the stripper to sit on the fiberglass for 2 to 3 minutes to dissolve the paint. If it sits much longer, it can damage the fiberglass, so be alert.
Scrape off the dissolved paint with a putty knife, taking care not to gouge the fiberglass surface. Use a nylon brush to remove the stripper if you're dealing with a heavily textured surface, or if the surface contains small areas that the putty knife cannot reach. Repeat the process on any patches of paint missed with the first stripping.
Rub the stripped fiberglass with a kitchen scrubbing pad dampened with denatured alcohol, to neutralize the chemical stripper.
Wipe stripper residue from the fiberglass surface with a rag. Go over the surface with a second, clean rag and examine the rag after wiping for any signs of chemical stripper residue. If you notice any signs of the stripper, apply the alcohol again and repeat the removal process until no signs of the stripper remain when you wipe the rag across the fiberglass surface.
Wait two hours for the fiberglass surface to dry and then sand it smooth for application of a new paint layer.