Virtually all liquids can be maintained for some time in a supercooled state, that is, at temperatures below their equilibrium melting temperatures, before eventually crystallizing. If cooled sufficiently quickly, some of these liquids will solidify into an amorphous solid, upon passing their glass transition temperature. Studies of these supercooled liquids reveal a considerable diversity in behaviour in their dynamical properties, particularly the viscosity. Angell characterized this in terms of their kinetic fragility. Previous synchrotron X-ray scattering studies have shown an increasing degree of short- and medium-range order that develops with increased supercooling. Here we demonstrate from a study of several metallic glass-forming liquids that the rate of this structural ordering as a function of temperature correlates with the kinetic fragility of the liquid, demonstrating a structural basis for fragility.