Introducing geodesic currents, Bonahon described a pairing I: T(S) x T(S) -> R on the Teichmüller space T(S) of a closed surface S. We consider a natural generalization to a pairing J : QF(S) x QF(S) -> R on quasifuchsian space QF(S). By naturality, it follows that the extended mapping class group of the surface S preserves J. We prove that the group of maps that preserve J not only contains, but is equal to the extended mapping class group of the surface. This is joint work with R. Canary.