  Stein kernels are a way of comparing probability distributions, defined via
integration by parts formulas. We provide two constructions of Stein kernels in
free probability. One is given by an explicit formula, and the other via free
Poincar\'e inequalities. In particular, we show that unlike in the classical
setting, free Stein kernels always exist. As corollaries, we derive new bounds
on the rate of convergence in the free CLT, and a strengthening of a
characterization of the semicircular law due to Biane.
