Hubble Space Telescope observations reveal that the density of stars in most elliptical galaxies rises toward the center in a power-law cusp. Many of these galaxies also contain central dark objects, possibly supermassive black holes. The gravitational force from a steep cusp or black hole will destroy most of the box orbits that constitute the "backbone" of a triaxial stellar system. Detailed modeling demonstrates that the resulting chaos can preclude a self-consistent, strongly triaxial equilibrium. Most elliptical galaxies may therefore be nearly axisymmetric, either oblate or prolate.