  We introduce a new class of extended affine Lie algebras called Hamiltonian
Extended Lie Algebras(HEALAs). They are so called because the corresponding
derivation algebra is the classical Hamiltonian algebra. We classify the
irreducible integrable modules for the HEALA based on the classification of
irreducible Jet modules for the Hamiltonian algebra (both zero level and
non-zero level.
