  We study the interplay between regular and chaotic dynamics at the critical
point of a generic first-order quantum phase transition in an interacting boson
model of nuclei. A classical analysis reveals a distinct behavior of the
coexisting phases in a broad energy range. The dynamics is completely regular
in the deformed phase and, simultaneously, strongly chaotic in the spherical
phase. A quantum analysis of the spectra separates the regular states from the
irregular ones, assigns them to particular phases, and discloses persisting
regular rotational bands in the deformed region.
