  We investigate the statistics of stationary points in the sum of squares of
$N$ Gaussian random fields, which we call a "chi-squared" field. The behavior
of such a field at a point is investigated, with particular attention paid to
the formation of topological defects. An integral to compute the number density
of stationary points at a given field amplitude is constructed. We compute
exact expressions for the integral in various limits and provide code to
evaluate it numerically in the general case. We investigate the dependence of
the number density of stationary points on the field amplitude, number of
fields, and power spectrum of the individual Gaussian random fields. This work
parallels the work of Bardeen, Bond, Kaiser and Szalay, who investigated the
statistics of peaks of Gaussian random fields. A number of results for
integrating over matrices are presented in appendices.
