Silky sharks (Carcharhinus falciformis) represent a major component of global shark catch, both directly and as bycatch, and populations are declining as a result. An improved understanding of their movement ecology is needed to support conservation efforts. We deployed satellite and acoustic tags (2013–2018) and analyzed historical fisheries records (1997–2009), to investigate the spatial ecology of silky sharks in the central Indian Ocean and a large Marine Protected Area (MPA; 640,000 km2) around the Chagos Archipelago. We observed high fidelity to the MPA, and a sustained diurnal association with a seamount complex, with individuals moving off at night and returning at sunrise. Yet, we also observed large-scale divergent movements in two satellite tagged individuals and documented the furthest recorded displacement distance for a satellite tagged silky shark to date, with one individual moving from the MPA to the Kenyan coast—a displacement distance of 3,549 km (track distance ∼4,782 km). Silky sharks undertook diel vertical migrations and oscillatory diving behavior, spending > 99% of their time in the top 100 m, and diving to depths of greater than 300 m, overlapping directly with typical deployments of purse seine and longline sets in the Indian Ocean. One individual was recorded to a depth of 1,112 m, the deepest recorded silky shark dive to date. Individuals spent 96% of their time at liberty within water temperatures between 24 and 30°C. Historic fisheries data revealed that silky sharks were a major component of the shark community around the archipelago, representing 13.69% of all sharks caught by longlines before the fishery closed in 2010. Over half (55.88%) of all individuals caught by longlines and purse seiners were juveniles. The large proportion of juveniles, coupled with the high site fidelity and residence observed in some individuals, suggests that the MPA could provide considerable conservation benefits for silky sharks, particularly during early life-history stages. However, their high mobility potential necessitates that large MPAs need to be considered in conjunction with fisheries regulations and conservation measures in adjacent EEZs and in areas beyond national jurisdiction.