We use linear rheology and multispeckle dynamic light scattering (MDLS) to investigate the aging of a gel composed of multilamellar vesicles. Light scattering data indicate rearrangement of the gel through an unusual ultraslow ballistic motion. A dramatic slowdown of the dynamics with sample age $t_{w}$ is observed for both rheology and MDLS, the characteristic relaxation time scaling as $t_{w}^{\mu}$. We find the same aging exponent $\mu =0.78$ for both techniques, suggesting that they probe similar physical processes, that is the relaxation of applied or internal stresses for rheology or MDLS, respectively. A simple phenomenological model is developed to account for the observed dynamics.