  We propose a new Monte Carlo method called the pinhole trace algorithm for
{\it ab initio} calculations of the thermodynamics of nuclear systems. For
typical simulations of interest, the computational speedup relative to
conventional grand-canonical ensemble calculations can be as large as a factor
of one thousand. Using a leading-order effective interaction that reproduces
the properties of many atomic nuclei and neutron matter to a few percent
accuracy, we determine the location of the critical point and the liquid-vapor
coexistence line for symmetric nuclear matter with equal numbers of protons and
neutrons. We also present the first {\it ab initio} study of the density and
temperature dependence of nuclear clustering.
