Flows in the ocean are driven either by atmospheric forces or by small-scale internal disturbances that are inherently chaotic. We use computer simulation results to show that these chaotic oceanic disturbances can attain spatial scales large enough to alter the motion of Earth's pole of rotation. Given their size and unpredictable nature, the chaotic signals are a source of uncertainty when interpreting observed year-to-year polar motion changes in terms of other processes in the Earth system.