Several aspects of perception, particularly those pertaining to vision, are closely linked to the occipital alpha (alpha) rhythm. However, how the alpha rhythm relates to the activity of neurons that convey primary visual information is unknown. Here we show that in behaving cats, thalamocortical neurons in the lateral geniculate nucleus (LGN) that operate in a conventional relay-mode form two groups where the cumulative firing is subject to a cyclic suppression that is centered on the negative alpha rhythm peak in one group and on the positive peak in the other. This leads to an effective temporal framing of relay-mode output and results from phasic inhibition from LGN interneurons, which in turn are rhythmically excited by thalamocortical neurons that exhibit high-threshold bursts. These results provide a potential cellular substrate for linking the alpha rhythm to perception and further underscore the central role of inhibition in controlling spike timing during cognitively relevant brain oscillations.