  Using Krasnov's formulation of General Relativity (GR), we develop a
lightcone ansatz for self-dual gravity (along with linearized anti-self-dual
perturbations) in the Poincare patch of de Sitter space. This amounts to a
generalization of Plebanski's "second heavenly equation" to non-zero
cosmological constant. The only interaction vertices are cubic ones, found
previously by Metsaev in a bottom-up lightcone approach. We point out a special
feature of these vertices, which leads to "almost conservation" of energy at
each successive order in perturbation theory, despite the time-dependent de
Sitter background. Since we embed the lightcone variables into a full spacetime
metric, the solutions have a clear geometric interpretation. In particular,
this allows us to read off boundary data on both the past and future horizons
of a causal (static) patch. In this way, we add self-dual GR to the program of
defining & computing scattering amplitudes in a causal patch of de Sitter
space.
