By means of quantum Monte Carlo (QMC) calculations from first-principles, we study the ground-state properties of the narrowest zigzag graphene nanoribbon with an infinite linear acene structure. We show that this quasi-one-dimensional system is correlated and its ground state is made of localized π electrons whose spins are antiferromagnetically ordered. The antiferromagnetic (AFM) stabilization energy [36(3) meV per carbon atom] and the absolute magnetization [1.13(0.11) μB per unit cell] predicted by QMC are sizable, and they suggest the survival of antiferromagnetic correlations above room temperature. These values can be reproduced to some extent by density functional theory (DFT) within the DFT+U framework or by using hybrid functionals. Based on our QMC results, we then provide the strength of Hubbard repulsion in DFT+U suitable for this class of systems.