Henson (1996) provided a number of demonstrations of error patterns in serial recall that contradict chaining models. One such error pattern concerned when participants make intrusions from prior lists: Rather than originating from random positions in the prior list, intrusions tend to be recalled in the same position as their position in the prior list, a finding which led to the endorsement of positional models of serial recall. However, all of the demonstrations of positional intrusions occurred in designs in which relatively small sets of items were repeatedly employed as stimuli. In recent years, a number of investigations have found evidence for chaining in designs in which large sets of items are employed and items are never reused across trials (open sets). We conducted 2 experiments using open sets of items to test whether a pure chaining model is a viable model for open-set conditions. Both experiments revealed that intrusions from the immediately preceding list exhibited a strong tendency to be output in the same position as their position in the prior list, suggesting the usage of positional representations in open-set designs. A chaining model that lacks positional representations provides an inadequate account of serial recall in open-set conditions.