We define star atoms as dressed quantum star graphs with Coulomb potentials on their edges. Focusing on star-lithium (star-Li), we study its classical and quantum mechanics. We find that, classically, star-Li is completely chaotic. Quantum mechanically, we identify an energy regime in which star-Li shows Wigner statistics, a hallmark of quantum chaos. Our results are relevant for identifying energy regimes and conditions under which quantum chaos may be identified in lithium and other multiply excited many-electron atoms.