Even during periods of fixation our eyes undergo small amplitude movements. These movements are thought to be essential to the visual system because neural responses rapidly fade when images are stabilized on the retina. The considerable recent interest in fixational eye movements (FEMs) has thus far concentrated on idealized experimental conditions with artificial stimuli and restrained head movements, which are not necessarily a suitable model for natural vision. Natural dynamic stimuli, such as movies, offer the potential to move beyond restrictive experimental settings to probe the visual system with greater ecological validity. Here, we study FEMs recorded in humans during the unconstrained viewing of a dynamic and realistic visual environment, revealing that drift trajectories exhibit the properties of a random walk with memory.