We theoretically show how to obtain a long one-dimensional crystal near its quantum ground state. We rely on an evaporative cooling scheme applicable to many-body systems with nonzero-ranged interactions. Despite the absence of periodic potentials, the final state is a crystal which exhibits long-range spatial order. We describe the scheme thermodynamically, applying the truncated Boltzmann distribution to the collective excitations of the chain, and show that it leads to a novel quasi-equilibrium many-body state. For longer chains, comprising about 1000 atoms, we emphasize the quasi-universality of the evaporation curve. Such exceptionally long 1D crystals are only accessible deep in the quantum regime. We perform our analysis on the example of an initially thermal chain of circular Rydberg atoms confined to a one-dimensional (1D) geometry. Our scheme may be applied to other quantum systems with long-ranged interactions such as polar molecules.