  We construct a Lorentz and generally covariant, polynomial action for free
chiral $p-$forms, classically equivalent to the Pasti-Sorokin-Tonin (PST)
formulation. The minimal set up requires introducing an auxiliary $p-$form on
top of the physical gauge $p-$form and the PST scalar. The action enjoys
multiple duality symmetries, including those that exchange the roles of
physical and auxiliary $p-$form fields. Actions of the same type are available
for duality-symmetric formulations, which is demonstrated on the example of the
electromagnetic field in four dimensions. There, the degrees of freedom of a
single Maxwell field are described employing four distinct vector gauge fields
and a scalar field.
