  We consider Chern-Simons actions of Abelian tensor hierarchy of $p$-form
gauge fields in four-dimensional ${\cal N}=1$ supergravity. Using conformal
superspace formalism, we solve the constraints on the field strengths of the
$p$-form gauge superfields in the presence of the tensor hierarchy. The
solutions are expressed by the prepotentials of the $p$-form gauge superfields.
We show the internal and superconformal transformation laws of the
prepotentials. The descent formalism for the Chern-Simons actions is exhibited.
