We have combined single crystal neutron and x-ray diffractions to investigate the magnetic and crystal structures of the honeycomb lattice Na_2IrO_3. The system orders magnetically below 18.1(2) K with Ir^4+ ions forming zigzag spin chains within the layered honeycomb network with ordered moment of 0.22(1) μ_B/Ir site. Such a configuration sharply contrasts the Néel or stripe states proposed in the Kitaev-Heisenberg model. The structure refinement reveals that the Ir atoms form nearly ideal 2D

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... oneycomb lattice while the IrO_6 octahedra experience a trigonal distortion that is critical to the ground state. The results of this study provide much-needed experimental insights into the magnetic and crystal structure crucial to the understanding of the exotic magnetic order and possible topological characteristics in the 5d-electron based honeycomb lattice.