We report a study of the connections between classical dynamics and quantum structure based on the lithium Stark spectrum. The system undergoes a transition to chaos as the energy or field is increased. We employ scaled-energy spectroscopy and closed-orbit theory to relate the photoabsorption spectrum to classical orbits. Bifurcations of closed orbits provide a semiclassical interpretation of the spectrum as it evolves from a simple sinusoidal modulation at positive energy to a discrete spectrum below the classical ionization limit. The system is compared with the closely related, but completely regular, hydrogen Stark system. The differences between their spectra and the development of chaos in lithium can be understood in terms of scattering of recurrences from one closed orbit to another by the alkali-metal core.