  We demonstrate the existence of an infinite number of local commuting charges
for classical solutions of the string sigma model on AdS_5 x S^5 associated
with a certain circular three-spin solution spinning with large angular momenta
in three orthogonal directions on the five-sphere. Using the AdS/CFT
correspondence we find agreement to one-loop with the tower of conserved higher
charges in planar N=4 super Yang-Mills theory associated with the dual
composite single-trace operator in the highest weight representation
(J_1,J_2,J_2) of SO(6). The agreement can be explained by the presence of
integrability on both sides of the duality.
