TOPOLOGICAL defects in the geometry of space-time (such as cosmic strings) may have played an important role in the evolution of the early Universe, by supplying initial density fluctuations which seeded the clusters of galaxies that we see today(1). The formation of cosmic strings during a symmetry-breaking phase transition shortly after the Big Bang is analogous to vortex creation in liquid helium following a rapid transition into the superfluid state; the underlying physics of this cosmological defect-forming process (known as the Kibble mechanism(1)) should therefore be accessible in He-4 following rapid quenching to the superfluid state(2), lending qualitative support to Kibble’s contention that topological defects are generated by such phase transitions. Here we quantify this process by using an exothermic neutron-induced nuclear reaction to heat small volumes of superfluid He-3 above the superfluid transition temperature, and then measuring the deficit in energy released as these regions of normal liquid pass back into the superfluid state. By ascribing this deficit to the formation of a tangle of vortices, we are able to infer the resulting vortex density; we find that this agrees very well with the predictions of Zurek’s modification(3) of the original Kibble mechanism(1).