  We give holomorphic Chern-Simons-like action functionals on supertwistor
space for self-dual supergravity theories in four dimensions, dealing with
N=0,...,8 supersymmetries, the cases where different parts of the R-symmetry
are gauged, and with or without a cosmological constant. The gauge group is
formally the group of holomorphic Poisson transformations of supertwistor space
where the form of the Poisson structure determines the amount of R-symmetry
gauged and the value of the cosmological constant. We give a formulation in
terms of a finite deformation of an integrable \dbar-operator on a supertwistor
space, i.e., on regions in CP^{3|8}. For N=0, we also give a formulation that
does not require the choice of a background.
