It is shown theoretically that a nonchiral, two-dimensional array of metallic spheres exhibits optical activity as manifested in calculations of circular dichroism. The metallic spheres occupy the sites of a rectangular lattice, and for off-normal incidence they show a strong circular-dichroism effect around the surface-plasmon frequencies. The optical activity is a result of the rectangular symmetry of the lattice, which gives rise to different polarization modes of the crystal along the two orthogonal primitive lattice vectors. These two polarization modes result in a net polar vector that forms a chiral triad with the wave vector and the vector normal to the plane of spheres. The formation of this chiral triad is responsible for the observed circular dichroism, although the structure itself is intrinsically nonchiral.