Colloidal silica gels are shown to stiffen with time, as demonstrated by both dynamic light scattering and bulk rheological measurements. Their elastic moduli increase as a power law with time, independent of particle volume fraction; however, static light scattering indicates that there are no large-scale structural changes. We propose that increases in local elasticity arising from bonding between neighboring colloidal particles can account for the strengthening of the network, while preserving network structure.