  Initial data for the spherically symmetric Einstein-Vlasov system is
constructed whose past evolution is regular and whose future evolution contains
a black hole. This is the first example of initial data with these properties
for the Einstein-matter system with a "realistic" matter model. One consequence
of the result is that there exists a class of initial data for which the ratio
of the Hawking mass $\open{m}=\open{m}(r)$ and the area radius $r$ is
arbitrarily small everywhere, such that a black hole forms in the evolution.
This result is in a sense analogous to the result for a scalar field. Another
consequence is that there exist black hole initial data such that the solutions
exist for all Schwarzschild time $t\in (-\infty,\infty)$.
