Many of the world's most important fisheries are experiencing increases in illegal fishing, undermining efforts to sustainably conserve and manage fish stocks. A major challenge to ending illegal, unreported, and unregulated (IUU) fishing is improving our ability to identify whether a vessel is fishing illegally and where illegal fishing is likely to occur in the ocean. However, monitoring the oceans is costly, time-consuming, and logistically challenging for maritime authorities to patrol. To address this problem, we use vessel tracking data and machine learning to predict illegal fishing on the Patagonian Shelf, one of the world's most productive regions for fisheries. Specifically, we focus on Chinese fishing vessels, which have consistently fished illegally in this region. We combine vessel location data with oceanographic seascapes -- classes of oceanic areas based on oceanographic variables -- as well as other remotely sensed oceanographic variables to train a series of machine learning models of varying levels of complexity. These models are able to predict whether a Chinese vessel is operating illegally with 69-96% confidence, depending on the year and predictor variables used. These results offer a promising step towards preempting illegal activities, rather than reacting to them forensically.