The optical signal in a hollow core anti-resonant fibre propagates in an air core surrounded by a single ring of anti-resonant non-touching tubes. Guidance is based on an anti-resonant effect from the thin glass membranes of the tubes. The extremely low overlap of guided power with the surrounding silica, less than 2×10-5, added to the mode effective area, confers to this fibre design a record material non-linearity.