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  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.