At low temperatures, the electrons in most layered transition-metal chalcogenides undergo a phase transition into an interesting, highly-ordered state called the charge-density-wave (CDW), in which the electron density spontaneously acquires a weak, periodic spatial modulation. In a small subset of materials, the CDW state is destroyed and replaced by the superconducting state. The recent discovery of superconductivity in the titanium selenide CuxTiSe2 provides a nearly ideal system to investigate the competition between the two states, which involve different ways to pair electrons. Angle-resolved photoemission spectroscopy (ARPES) measures the angular distribution of photo-ejected electrons. PCCM researchers and collaborators [1] have applied this powerful technique to measure the energy dispersion of electrons in CuxTiSe2 and to map out its Fermi Surface (FS, see figure). Results from a series of samples reveal the evolution of states participating in CDW formation, and the growth of the superconducting gap. They find [1,2] that CDW formation does not follow the usual "nesting" pattern involving parallel FS segments. Instead, it originates from pairing between electron and holes to form excitons, with electron-phonon interaction playing a complementary role. A single parameter -- the density of states -- appears to dictate whether the CDW state or superconductivity dominates.