We report on the discovery of periodic coronal rain in an off-limb sequence of Solar Dynamics Observatory/Atmospheric Imaging Assembly images. The showers are co-spatial and in phase with periodic (6.6 hr) intensity pulsations of coronal loops of the sort described by Auchère et al. and Froment et al. These new observations make possible a unified description of both phenomena. Coronal rain and periodic intensity pulsations of loops are two manifestations of the same physical process: evaporation/condensation cycles resulting from a state of thermal nonequilibrium. The fluctuations around coronal temperatures produce the intensity pulsations of loops, and rain falls along their legs if thermal runaway cools the periodic condensations down and below transition-region temperatures. This scenario is in line with the predictions of numerical models of quasi-steadily and footpoint heated loops. The presence of coronal rain—albeit non-periodic—in several other structures within the studied field of view implies that this type of heating is at play on a large scale.