We investigated how attention shifts from one object to another by recording neuronal activity in the primary visual cortex. Monkeys performed a contour-grouping task in which they had to select a target curve and ignore a distractor curve. Some trials required a shift of attention, because the target and distractor curves were switched during the course of the trial. We monitored the dynamics of this attention shift in area V1, in which neuronal responses evoked by the target curve are stronger than those evoked by the distractor. The reallocation of attention was associated with a rapid and strong enhancement of responses to the newly attended curve, followed, after approximately 60 ms, by a weaker suppression of responses to the curve from which attention was removed. We conclude that attention can be rapidly allocated to a new object before it disengages from the previously attended one.