Lateralization is widespread throughout the animal kingdom [1-7] and can increase task efficiency via shortening reaction times and saving on neural tissue [8-16]. However, lateralization might be costly because it increases predictability [17-21]. In predator-prey interactions, for example, predators might increase capture success because of specialization in a lateralized attack, but at the cost of increased predictability to their prey, constraining the evolution of lateralization. One unexplored mechanism for evading such costs is group hunting: this would allow individual-level specialization, while still allowing for group-level unpredictability. We investigated this mechanism in group hunting sailfish, Istiophorus platypterus, attacking schooling sardines, Sardinella aurita. During these attacks, sailfish alternate in attacking the prey using their elongated bills to slash or tap the prey [22-24]. This rapid bill movement is either leftward or rightward. Using behavioral observations of identifiable individual sailfish hunting in groups, we provide evidence for individual-level attack lateralization in sailfish. More strongly lateralized individuals had a higher capture success. Further evidence of lateralization comes from morphological analyses of sailfish bills that show strong evidence of one-sided micro-teeth abrasions. Finally, we show that attacks by single sailfish are indeed highly predictable, but predictability rapidly declines with increasing group size because of a lack of population-level lateralization. Our results present a novel benefit of group hunting: by alternating attacks, individual-level attack lateralization can evolve, without the negative consequences of individual-level predictability. More generally, our results suggest that group hunting in predators might provide more suitable conditions for the evolution of strategy diversity compared to solitary life.