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It is a classic result in cognitive science that chess masters can recall briefly presented positions better than weaker players when these positions are meaningful, but that their superiority disappears with random positions. However, Gobet and Simon (1996a) have recently shown that there is a skill effect in the recall of random chess positions as well. The impact of this result for theories of expert memory is discussed, and it is shown that chunk-based theories predict such a skill difference. CHREST, a computational, chunk-based model of chess expertise based on the EPAM theory of cognition, accounts for the skill differences well. The model's performance is also compared with human data where the role of presentation time for random positions is systematically varied from 1 s to 60 s. Preliminary results show that the model captures the main features of the human data, but also point to additional work for estimating the value of a few parameters with more precision.