  The Universe may pass through an effectively matter-dominated epoch between
inflation and Big Bang Nucleosynthesis during which gravitationally bound
structures can form on subhorizon scales. In particular, the inflaton field can
collapse into inflaton halos, forming "large scale" structure in the very early
universe. We combine N-body simulations with high-resolution zoom-in regions in
which the non-relativistic Schr\"odinger-Poisson equations are used to resolve
the detailed, wave-like structure of inflaton halos. Solitonic cores form
inside them, matching structure formation simulations with axion-like particles
in the late-time universe. We denote these objects \textit{inflaton stars}, by
analogy with boson stars. Based on a semi-analytic formalism we compute their
overall mass distribution which shows that some regions will reach
overdensities of $10^{15}$ if the early matter-dominated epoch lasts for 20
$e$-folds. The radii of the most massive inflaton stars can shrink below the
Schwarzschild radius, suggesting that they could form primordial black holes
prior to thermalization.
