One view of the high-transition-temperature (high-T-c) copper oxide superconductors is that they are conventional superconductors where the pairing occurs between weakly interacting quasi-particles (corresponding to the electrons in ordinary metals), although the theory has to be pushed to its limit(1). An alternative view is that the electrons organize into collective textures (for example, charge and spin stripes) which cannot be 'mapped' onto the electrons in ordinary metals. Understanding the properties of the material would then need quantum field theories of objects such as textures and strings, rather than point-like electrons(2-6). In an external magnetic field, magnetic flux penetrates type II superconductors via vortices, each carrying one flux quantum(7). The vortices form lattices of resistive material embedded in the non-resistive superconductor, and can reveal the nature of the ground state-for example, a conventional metal or an ordered, striped phase-which would have appeared had superconductivity not intervened, and which provides the best starting point for a pairing theory. Here we report that for one high-T-c superconductor, the applied field that imposes the vortex lattice also induces 'striped' antiferromagnetic order. Ordinary quasiparticle models can account for neither the strength of the order nor the nearly field-independent antiferromagnetic transition temperature observed in our measurements.