We have measured the precession frequency of a vortex lattice in a Bose-Einstein condensate of Rb87 atoms. The observed mode corresponds to a collective motion in which all the vortices in the array are tilted by a small angle with respect to the z axis (the symmetry axis of the trapping potential) and synchronously rotate about this axis. This motion corresponds to excitation of a Kelvin wave along the core of each vortex and we have verified that it has the handedness expected for such helical waves, i.e., precession in the opposite sense to the rotational flow around the vortices.