A chair that can be mounted to a bleacher comprises a dual-pivot structure to enable movement of a seat between an up position, wherein the seat compactly fits within the bleacher envelope, and a down position, wherein the seat is substantially aligned with the bleacher and located at a suitable seating height. The chair includes single-piece, injection molded bleacher bases, which are composed of a “no-break”, fade-resistant plastic and include strategically positioned strengthening ribs. Additional embodiments of the chair comprise a clip-on bleacher base for removably mounting the chair to the bleacher and riser bases and floor bases that can be affixed to a riser portion and a floor portion, respectively, of a step structure.