For material spontaneously generating fission chains, the arrival times of neutron and gamma-ray counts create a clustering pattern distinctly different from a random source. A theory for the time interval distribution between counts is given. As well as the distribution of nearest-neighbor counts, we give the general distributions for all n'th-neighbor intervals. The sum of these distributions gives the Rossi correlation function. This theory supplies the direct link between the experimentally measured quantities and the theory of the Rossi correlation function.