  In this letter we establish Yangian symmetry of planar N=4 super-Yang-Mills
theory. We prove that the classical equations of motion of the model close onto
themselves under the action of Yangian generators. Moreover we propose an
off-shell extension of our statement which is equivalent to the invariance of
the action and prove that it is exactly satisfied. We assert that our
relationship serves as a criterion for integrability in planar gauge theories
by explicitly checking that it applies to integrable ABJM theory but not to
non-integrable N=1 super-Yang-Mills theory.
