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 t(z) 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.