  We semiclassicalise the theory of quantum group principal bundles to the
level of Poisson geometry. The total space $X$ is a Poisson manifold with
Poisson-compatible contravariant connection, the fibre is a Poisson-Lie group
in the sense of Drinfeld with bicovariant Poisson-compatible contravariant
connection, and the base has an inherited Poisson structure and
Poisson-compatible contravariant connection. The latter are known to be the
semiclassical data for a quantum differential calculus. The theory is
illustrated by the Poisson level of the $q$-Hopf fibration on the standard
$q$-sphere. We also construct the Poisson level of the spin connection on a
principal bundle.
