  Many integrable systems can be reformulated as holomorphic vector bundles on
twistor space. This is a powerful organizing principle in the theory of
integrable systems. One shortcoming is that it is formulated at the level of
the equations of motion. From this perspective, it is mysterious that
integrable systems have Lagrangians. In this paper, we study a Chern-Simons
action on twistor space and use it to derive the Lagrangians of some integrable
sigma models. Our focus is on examples that come from dimensionally reduced
gravity and supergravity. The dimensional reduction of general relativity to
two spacetime dimensions is an integrable coset sigma model coupled to a
dilaton and 2d gravity. The dimensional reduction of supergravity to two
spacetime dimensions is an integrable coset sigma model coupled to matter
fermions, a dilaton, and 2d supergravity. We derive Lax operators and
Lagrangians for these 2d integrable systems using the Chern-Simons theory on
twistor space. In the supergravity example, we use an extended setup in which
twistor Chern-Simons theory is coupled to a pair of matter fermions.
