The strength of ionic bonds is essentially unknown, despite their widespread occurrence in natural and man-made assemblies. Here, we use single-molecule force spectroscopy to measure their strength directly. We disrupt a complex between two oppositely charged polyelectrolyte chains and find two modes of rupture: one ionic bond at a time, or cooperative rupture of many bonds at once. For both modes, disruption of the ionic bonds can be described quantitatively as an activated process. The height of the energy barrier is not only lowered by added salt, but also by the applied force. We extract unperturbed ionic bond lifetimes that range from milliseconds for single ionic bonds at high salt concentration to tens of years for small complexes of five ionic bonds at low salt concentration.