  A new closure of the BBGKY hierarchy is developed, which results in a
convergent kinetic equation that provides a rigorous extension of plasma
kinetic theory into the regime of strong Coulomb coupling. The approach is
based on a single expansion parameter which enforces that the exact equilibrium
limit is maintained at all orders. Because the expansion parameter does not
explicitly depend on the range or the strength of the interaction potential,
the resulting kinetic theory does not suffer from the typical divergences at
short and long length scales encountered when applying the standard kinetic
equations to Coulomb interactions. The approach demonstrates that particles
effectively interact via the potential of mean force and that the range of this
force determines the size of the collision volume. When applied to a plasma,
the collision operator is shown to be related to the effective potential theory
[Baalrud and Daligault, Phys. Rev. Lett 110, 235001 (2013)]. The relationship
between this and previous kinetic theories is discussed.
