The formation of very wide binary systems(1-3), such as the a Centauri system with Proxima (also known as a Centauri C) separated from a Centauri (which itself is a close binaryA/B) by 15,000 astronomical units(4) (1 AU is the distance from Earth to the Sun), challenges current theories of star formation, because their separation can exceed the typical size of a collapsing cloud core. Various hypotheses have been proposed to overcome this problem, including the suggestion that ultrawide binaries result from the dissolution of a star cluster-when a cluster star gravitationally captures another, distant, cluster star(5-7). Recent observations have shown that very wide binaries are frequently members of triple systems(8,9) and that close binaries often have a distant third companion(10-12). Here we report N-body simulations of the dynamical evolution of newborn triple systems still embedded in their nascent cloud cores that match observations of very wide systems(13-15). We find that although the triple systems are born very compact-and therefore initially are more protected against disruption by passing stars(16,17)-they can develop extreme hierarchical architectures on timescales of millions of years as one component is dynamically scattered into a very distant orbit. The energy of ejection comes from shrinking the orbits of the other two stars, often making them look from a distance like a single star. Such loosely bound triple systems will therefore appear to be very wide binaries.