  We study symmetries of the quantized open twistor string. In addition to
global PSL(4|4) symmetry, we find non-local conserved currents. The associated
non-local charges lead to Ward identities which show that these charges
annihilate the string gluon tree amplitudes, and have the same form as
symmetries of amplitudes in N=4 super conformal Yang Mills theory. We describe
how states of the open twistor string form a realization of the PSL(4|4)
Yangian superalgebra.
