The visual system imposes structure onto incoming information, by grouping image elements of a single object together, and by segregating them from elements that belong to other objects and the background. One influential theory holds that the code for grouping and segmentation is carried by the synchrony of neuronal discharges on a millisecond time scale. We tested this theory by recording neuronal activity in the primary visual cortex (area V1) of monkeys engaged in a contour-grouping task. We found that synchrony was unrelated to contour grouping. The firing rates of V1 neurons are also correlated across trials. We demonstrate that this rate covariation is mainly determined by fluctuations in visual attention. Moreover, we show that rate covariation depends on perceptual grouping, as it is strongest between neurons that respond to features of the same object.