We use multispeckle dynamic light scattering to measure the dynamic structure factor, f(q,tau), of gels formed by aggregation of colloids. Although the gel is an elastic solid, f(q,tau) nearly completely decays on long time scales, with an unusual form, f(q, tau) approximately exp{-(tau/tau(f))(mu)}, with mu approximately 1.5 and with tau(f) proportional variant q(-1). A model for restructuring of the gel with aging correctly accounts for this behavior. Aging leads to a dramatic increase in tau(f); however, all data can be scaled on a single master curve, with tau(f) asymptotically growing linearly with age. This behavior is strikingly similar to that predicted for aging in disordered glassy systems, offering convincing proof of the universality of these concepts.