  We propose that the complete planar S-matrix of N=4 super Yang-Mills -
including all N^kMHV partial amplitudes to all loops - is equivalent to the
correlation function of a supersymmetric Wilson loop in twistor space.
Remarkably, the entire classical S-matrix arises from evaluating the
correlation function in the self-dual sector, while the expansion of the
correlation function in powers of the Yang-Mills coupling constant provides the
loop expansion of the amplitudes. We support our proposal with explicit
computations of the n particle NMHV and NNMHV trees, the integrands of the
1-loop MHV and NMHV amplitudes, and the n particle 2-loop MHV amplitude. These
calculations are performed using the twistor action in axial gauge. In this
gauge, the Feynman diagrams of the correlation function are the planar duals of
the usual MHV diagrams for the scattering amplitude. The results are presented
in the form of a sum of products of dual superconformal invariants in
(momentum) twistor space, and agree with the expressions derived in
arXiv:1009.1854 directly from the MHV rules. The twistor space Wilson loop is a
natural supersymmetric generalization of the standard Wilson loop used to
compute MHV amplitudes. We show how the Penrose-Ward transform can be used to
determine a corresponding supersymmetrization on space-time.
