Biological membranes exhibit the ability to self-repair and dynamically change their shape while remaining impermeable. Yet, these defining features are difficult to reconcile with mechanical robustness. Here, we report on the spontaneous formation of a carbon nanoskin at the oil-water interface that uniquely combines self-healing attributes with high stiffness. Upon the diffusion-controlled self-assembly of a reactive molecular surfactant at the interface, a solid elastic membrane forms within seconds and evolves into a continuous carbon monolayer with a thickness of a few nanometers. This nanoskin has a stiffness typical for a 2D carbon material with an elastic modulus in bending of more than 40-100 GPa; while brittle, it shows the ability to self-heal upon rupture, can be reversibly reshaped, and sustains complex shapes. We anticipate such an unusual 2D carbon nanomaterial to inspire novel approaches towards the formation of synthetic cells with rigid shells, additive manufacturing of composites, and compartmentalization in industrial catalysis. Biological membranes exhibit the ability to self-repair and dynamically change their shape while remaining impermeable but these defining features are difficult to reconcile with mechanical robustness. Here, the authors report on the spontaneous formation of a carbon nanoskin at the oil-water interface that uniquely combines self-healing attributes with high stiffness.