  There exists no natural variational principle for the dynamics of abelian
p-form potentials with self-dual field strengths, also called chiral p-forms.
Relying on the PST method, we establish the general consistency condition for a
Lagrangian to describe a Lorentz invariant self-interacting chiral 2n-form in
4n+2 dimensions. For a generic n, we determine a canonical solution of this
condition for a quartic interaction Lagrangian of the 2n-form, and prove that
for the four-form in ten dimensions this interaction is unique. It generalizes
the corresponding Born-Infeld-like interaction of a chiral two-form in six
dimensions. We verify that under a dimensional reduction on a torus, this
interaction Lagrangian reduces to a combination of the two recently constructed
SO(2)-duality invariant quartic interactions for abelian three-form potentials
in eight dimensions. The potential relevance of our method for the type IIB
superstring effective action is discussed.
