Instructions
Look first at the design of the chair. Almost all fiberglass chairs follow the design pattern laid down by Saarinen and his colleague Charles Eames. The chair breaks down into two elements -- a seating "shell", molded in one piece, and a support structure - i.e., legs or a pedestal -- which is usually of a different material, most often metal. To see if the chair is molded in one piece, look over it for signs of joints and flex it to see if it moves as one unit. If a chair doesn't follow this pattern, it is unlikely to be fiberglass.
Pick up the chair to test its weight. Because fiberglass was designed for use in the aeronautical industry, it is very light, and so should the chair be.
Splash a bit of water on the chair, let it sit for a moment and wipe it off again. As fiberglass is water-resistant, this process should leave no mark on the chair, except perhaps little smudges to be cleaned a little.
Look for bright colors and textured surfaces, as these are both associated with fiberglass.