The air-water interface is perhaps the most common liquid interface. It covers more than 70 per cent of the Earth's surface and strongly affects atmospheric, aerosol and environmental chemistry. The air-water interface has also attracted much interest as a model system that allows rigorous tests of theory, with one fundamental question being just how thin it is. Theoretical studies have suggested a surprisingly short 'healing length' of about 3 angstroms (1 angstrom = 0.1 nm), with the bulk-phase properties of water recovered within the top few monolayers(1-3). However, direct experimental evidence has been elusive owing to the difficulty of depth-profiling the liquid surface on the angstrom scale. Most physical, chemical and biological properties of water, such as viscosity, solvation, wetting and the hydrophobic effect, are determined by its hydrogen-bond network. This can be probed by observing the lineshape of the OH-stretch mode, the frequency shift of which is related to the hydrogen-bond strength(4-6). Here we report a combined experimental and theoretical study of the air-water interface using surface-selective heterodyne-detected vibrational sum frequency spectroscopy to focus on the 'free OD' transition found only in the topmost water layer. By using deuterated water and isotopic dilution to reveal the vibrational coupling mechanism, we find that the free OD stretch is affected only by intramolecular coupling to the stretching of the other OD group on the same molecule. The other OD stretch frequency indicates the strength of one of the first hydrogen bonds encountered at the surface; this is the donor hydrogen bond of the water molecule straddling the interface, which we find to be only slightly weaker than bulk-phase water hydrogen bonds. We infer from this observation a remarkably fast onset of bulk-phase behaviour on crossing from the air into the water phase.