Topological properties of materials are of fundamental as well as practical importance1,2. Of particular interest are unconventional superconductors that break time-reversal symmetry, for which the superconducting state is protected topologically and vortices can host Majorana fermions with potential use in quantum computing3,4. However, in striking contrast to the unconventional A phase of superfluid 3He where chiral symmetry was directly observed5, identification of broken time-reversal symmetry of the superconducting order parameter, a key component of chiral symmetry, has presented a challenge in bulk materials. The two leading candidates for bulk chiral superconductors are UPt 3 (refs. 6,7,8) and Sr 2 RuO 4 (ref. 9), although evidence for broken time-reversal symmetry comes largely from surface-sensitive measurements. A long-sought demonstration of broken time-reversal symmetry in bulk Sr 2 RuO 4 is the observation of edge currents, which has so far not been successful10. The situation for UPt 3 is not much better. Here, we use vortices to probe the superconducting state in ultraclean crystals of UPt 3 . Using small-angle neutron scattering, a strictly bulk probe, we demonstrate that the vortices possess an internal degree of freedom in one of its three superconducting phases, providing direct evidence for bulk broken time-reversal symmetry in this material.