  We directly image Tkachenko waves in a vortex lattice in a dilute-gas
Bose-Einstein condensate. The low (sub-Hz) resonant frequencies are a
consequence of the small but nonvanishing elastic shear modulus of the
vortex-filled superfluid. The frequencies are measured for rotation rates as
high as 98% of the centrifugal limit for the harmonically confined gas.
Agreement with a hydrodynamic theory worsens with increasing rotation rate,
perhaps due to the increasing fraction of the volume displaced by the vortex
cores. We also observe two low-lying m=0 longitudinal modes at about 20 times
higher frequency.
