  The Killing tensor equation is a first order differential equation on
symmetric covariant tensors that generalises to higher rank the usual Killing
vector equation on Riemannian manifolds. We view this more generally as an
equation on any manifold equipped with an affine connection, and in this
setting derive its prolongation to a linear connection. This connection has the
property that parallel sections are in 1-1 correspondence with solutions of the
Killing equation. Moreover this connection is projectively invariant and is
derived entirely using the projectively invariant tractor calculus which
reveals also further invariant structures linked to the prolongation.
