The coarsening of a three-dimensional foam is studied with multiple light-scattering techniques. Scaling behavior is observed with the average bubble diameter growing in time as tz where z=0.45±0.05. Changes in the packing conditions during coarsening give rise to a dynamical process that also exhibits temporal scaling. Neighboring bubbles undergo sudden structural rearrangement events at a rate per unit volume that decays as t−y where y=2.0±0.2.