  We consider a free (2 k)-form gauge-field on a Euclidean (4 k + 2)-manifold.
The parameters needed to specify the action and the gauge-invariant observables
take their values in spaces with natural complex structures. We show that the
correlation functions can be written as a finite sum of terms, each of which is
a product of a holomorphic and an anti-holomorphic factor. The holomorphic
factors are naturally interpreted as correlation functions for a chiral (2
k)-form, i.e. a (2 k)-form with a self-dual (2 k + 1)-form field strength,
after Wick rotation to a Minkowski signature.
