I suggest that most discussions of intentional systems have overlooked an important aspect of living organisms: the intrinsic goal-directedness inherent in the behaviour of living eukaryotic cells. This goal directedness is nicely displayed by a normal cell’s ability to rearrange its own local material structure in response to damage, nutrient distribution or other aspects of its individual experience. While at a vastly simpler level than intentionality at the human cognitive level, I propose that this basic capacity of living things provides a necessary building block for cognition and high-order intentionality, because the neurons that make up vertebrate brains, like most cells in our body, embody such capacities. I provisionally dub the capacities in question “nano-intentionality”: a microscopic form of “aboutness”. The form of intrinsic intentionality I propose is thoroughly materialistic, fully compatible with known biological facts, and derived non-mysteriously through evolution. Crucially, these capacities are not shared by any existing computers or computer components, and thus provide a clear, empirically-based distinction between brains and currently existing artificial information processing systems. I suggest that an appreciation of this aspect of living matter provides a potential route out of what may otherwise appear to be a hopeless philosophical quagmire confronting information-processing models of the mind.