  We study the competing order and chaos in a first-order quantum phase
transition with a high barrier. The boson model Hamiltonian employed,
interpolates between its U(5) (spherical) and SU(3) (deformed) limits. A
classical analysis reveals regular (chaotic) dynamics at low (higher) energy in
the spherical region, coexisting with a robustly regular dynamics in the
deformed region. A quantum analysis discloses, amidst a complicated
environment, persisting regular multiplets of states associated with partial
U(5) and quasi SU(3) dynamical symmetries.
