NaMoO2 was synthesized as a layered oxide from the reaction between the layered oxide Na2/3MoO2 and metal sodium. Its structure was determined from high-resolution powder X-ray diffraction, and it can be described as an alpha-NaFeO2 distorted structure in which sodium ions and molybdenum atoms occupy octahedral interstitial sites. Chains of "diamond-like" clusters of molybdenum were evidenced in the [MoO2] layers resulting from the Peierls distortion expected in a two-dimensional triangular lattice formed by transition metal atoms with a d(3) electronic configuration. Molybdenum-molybdenum distances as short as 2.58 angstrom were found in these clusters. The magnetic moment recorded at low temperatures and at room temperature showed that NaMoO2 presents a very low magnetic susceptibility compatible with the localization of the 4d electrons in the Mo-Mo bonds. This localization was confirmed by DFT calculation that showed the NaMoO2 was diamagnetic at 0 K. A sodium battery was built using NaMoO2 as the positive electrode material, and we found that sodium ions can be reversibly deintercalated and intercalated in NaMoO2, indicating that this compound is one of the many phases existing in the NaxMoO2 system.