Mapping and predicting the potential risk of fishing activities to large marine protected areas (MPAs), where management capacity is low but fish biomass may be globally important, is vital to prioritizing enforcement and maximizing conservation benefits. Drifting fish aggregating devices (dFADs) are a highly effective fishing method employed in purse seine fisheries that attract and accumulate biomass fish, making fish easier to catch. However, dFADs are associated with several negative impacts, including high bycatch rates and lost or abandoned dFADs becoming beached on sensitive coastal areas (e.g., coral reefs). Using Lagrangian particle modeling, we determined the potential transit of dFADs in a large MPA around the Chagos Archipelago in the central Indian Ocean. We then quantified the risk of dFADs beaching on the archipelago's reefs and atolls and determined the potential for dFADs to pass through the MPA, accumulate biomass while within, and export it into areas where it can be legally fished (i.e., transit). Over one-third (37.51%) of dFADs posed a risk of either beaching or transiting the MPA for >14 days, 17.70% posed a risk of beaching or transiting the MPA for >30 days, and 13.11% posed a risk of beaching or transiting the MPA for >40 days. Modeled dFADs deployed on the east and west of the perimeter were more likely to beach and have long transiting times (i.e., posed the highest risk). The Great Chagos Bank, the largest atoll in the archipelago, was the most likely site to be affected by dFADs beaching. Overall, understanding the interactions between static MPAs and drifting fishing gears is vital to developing suitable management plans to support enforcement of MPA boundaries and the functioning and sustainability of their associated biomass.