The age of globular clusters and the stars they contain is thought to be on the order of 10 billion years. Neutron stars are believed to form via supernova explosions of massive stars, and their progenitor stars have very short volutionary lifetimes, so neutron star production in globular clusters ought to have ceased billions of years ago. Neutron stars move at high velocities, which are probably the result of large kicks they receive during their formation. Their speeds are more than sufficient for neutron stars to escape from globular clusters within thousands of years. Hence, globular clusters should contain few, if any, neutron stars. Yet, globular clusters typically contain many neutron stars. This suggests that globular clusters may be much younger than generally thought.