Charge Order Along Mirror Twin Boundaries in MoSe$_2$

One-dimensional systems generically exhibit charge ordering, in which the lattice develops a periodic modulation, through the Peierls instability. The argument assumes an infinite system size. What happens as this assumption is relaxed? Using atomically-resolved scanning tunneling microscopy and atomic force microscopy on semiconducting monolayers of molybdenum diselenide (MoSe$_2$) we see conducting edge states along one-dimensional mirror twin boundaries. Remarkably, these edge states, which are approximately thirty to sixty atoms in length, develop their own energy gap via charge ordering. Self-consistently solving a Hubbard model we demonstrate that these systems exactly at the crossover from charge ordering to quantum well physics, demonstrating features of both simultaneously.