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 UPt3 (refs. 6,7,8) and Sr2RuO4 (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 Sr2RuO4 is the observation of edge currents, which has so far not been successful10. The situation for UPt3 is not much better. Here, we use vortices to probe the superconducting state in ultraclean crystals of UPt3. 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.