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 uncertainties(1). There are almost no nuclear data for neutron-induced reactions of the radioactive nucleus Zr-88, despite its importance as a diagnostic for nuclear security. Here, by exposing Zr-88 to the intense neutron flux of a nuclear reactor, we determine that Zr-88 has a thermal neutron capture cross-section of 861,000 +/- 69,000 barns (1 sigma uncertainty), which is five orders of magnitude larger than the theoretically predicted value of 10 barns(2). 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 10(5) barns(3-6) are Xe-135 (2.6 x 10(6) barns), a fission product that was first discovered as a poison in early reactors(7,8), and Gd-157 (2.5 x 10(5) barns), which is used as a detector material(9,10), a burnable reactor poison(11) and a potential medical neutron capture therapy agent(12). In the case of Zr-88 neutron capture, both the target and the product (Zr-89) nuclei are radioactive and emit intense gamma-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.