  We found an analytical solution for the vortex structure in a rapidly
rotating trapped Bose-Einstein condensate in the lowest Landau level
approximation. This solution is exact in the limit of a large number of
vortices and is obtained for the case of anisotropic harmonic potential. For
the case of symmetric harmonic trap when the rotation frequency is equal to the
trapping frequency, the solution coincides with the Abrikosov triangle vortex
lattice in type-II superconductors.
  In a general case the coarse grained density is found to be close to the
Thomas-Fermi profile, except the vicinity of edges of a condensate cloud.
