The probability that a nucleus will absorb a neutron-the neutron capture cross-section-is important to many areas of nuclear science, including stellar nucleosynthesis, reactor performance, nuclear medicine and defence applications. Although neutron capture cross-sections have been measured for most stable nuclei, fewer results exist for radioactive isotopes, and statistical-model predictions typically have large uncertainties1. There are almost no nuclear data for neutron-induced reactions of the radioactive nucleus 88Zr, despite its importance as a diagnostic for nuclear security. Here, by exposing 88Zr to the intense neutron flux of a nuclear reactor, we determine that 88Zr has a thermal neutron capture cross-section of 861,000 ± 69,000 barns (1σ uncertainty), which is five orders of magnitude larger than the theoretically predicted value of 10 barns2. This is the second-largest thermal neutron capture cross-section ever measured and no other cross-section of comparable size has been discovered in the past 70 years. The only other nuclei known to have values greater than 105 barns3-6 are 135Xe (2.6 × 106 barns), a fission product that was first discovered as a poison in early reactors7,8, and 157Gd (2.5 × 105 barns), which is used as a detector material9,10, a burnable reactor poison11 and a potential medical neutron capture therapy agent12. In the case of 88Zr neutron capture, both the target and the product (89Zr) nuclei are radioactive and emit intense γ-rays upon decay, allowing sensitive detection of miniscule quantities of these radionuclides. This result suggests that as additional measurements with radioactive isotopes become feasible with the operation of new nuclear-science facilities, further surprises may be uncovered, with far-reaching implications for our understanding of neutron capture reactions.