The realization and control of large-scale quantum systems is an exciting frontier of modern physical science. Using a novel cold atom platform, we trap single neutral atoms in an array of optical tweezers, and use real-time feedback to prepare defect-free chains of tens of atoms in one dimension with a high fidelity and repetition rate. Excitation of the atoms to Rydberg states enables strong and tunable van der Waals interactions over long distances, which allows for engineering an Ising-type Hamiltonian with non-trivial spatial correlations between Rydberg atoms. Employing adiabatic transitions into crystalline states of Rydberg atoms, we study the properties of the system close to a phase transition. Furthermore, we study the quench dynamics of Rydberg crystals and uncover signatures of entanglement in Rydberg chains.