  We prove that every group ring of a non-abelian locally free group which is
the union of an ascending sequence of free groups is primitive. In particular,
every group ring of a countable non-abelian locally free group is primitive. In
addition, by making use of the result, we give a necessary and sufficient
condition for group rings of ascending HNN extensions of free groups to be
primitive, which extends the known result for the countable case to the general
cardinality case. In order to prove the main theorem, we state some
graph-theoretic results and apply them to to Formanek's method.
