Many behaviors exhibit ~24-h oscillations under control of an endogenous circadian timing system that tracks time of day via a molecular circadian clock. In the fruit fly, Drosophila melanogaster, most circadian research has focused on the generation of locomotor activity rhythms, but a fundamental question is how the circadian clock orchestrates multiple distinct behavioral outputs. Here, we have investigated the cells and circuits mediating circadian control of feeding behavior. Using an array of genetic tools, we show that, as is the case for locomotor activity rhythms, the presence of feeding rhythms requires molecular clock function in the ventrolateral clock neurons of the central brain. We further demonstrate that the speed of molecular clock oscillations in these neurons dictates the free-running period length of feeding rhythms. In contrast to the effects observed with central clock cell manipulations, we show that genetic abrogation of the molecular clock in the fat body, a peripheral metabolic tissue, is without effect on feeding behavior. Interestingly, we find that molecular clocks in the brain and fat body of control flies gradually grow out of phase with one another under free-running conditions, likely due to a long endogenous period of the fat body clock. Under these conditions, the period of feeding rhythms tracks with molecular oscillations in central brain clock cells, consistent with a primary role of the brain clock in dictating the timing of feeding behavior. Finally, despite a lack of effect of fat body selective manipulations, we find that flies with simultaneous disruption of molecular clocks in multiple peripheral tissues (but with intact central clocks) exhibit decreased feeding rhythm strength and reduced overall food intake. We conclude that both central and peripheral clocks contribute to the regulation of feeding rhythms, with a particularly dominant, pacemaker role for specific populations of central brain clock cells.