A classic question concerns whether humans can attend multiple locations or objects at once. Although it is generally agreed that the answer to this question is "yes," the limits on this ability are subject to extensive debate. According to one view, attentional resources can be flexibly allocated to a variable number of locations, with an inverse relationship between the number of selected locations and the quality of information processing at each location. Alternatively, these resources might be quantized in a "discrete" fashion that enables concurrent access to a small number of locations. Here, we report a series of experiments comparing these alternatives. In each experiment, we cued participants to attend a variable number of spatial locations and asked them to report the orientation of a single, briefly presented target. In all experiments, participants' orientation report errors were well-described by a model that assumes a fixed upper limit in the number of locations that can be attended. Conversely, report errors were poorly described by a flexible-resource model that assumes no fixed limit on the number of locations that can be attended. Critically, we showed that these discrete limits were predicted by cue-evoked neural activity elicited before the onset of the target array, suggesting that performance was limited by selection processes that began prior to subsequent encoding and memory storage. Together, these findings constitute novel evidence supporting the hypothesis that human observers can attend only a small number of discrete locations at an instant.