Disodium tetrafluoroargentate(II) (Na₂AgF₄) has been synthesized by the thermal decomposition of NaAg(III)F₄ in the presence of NaF. This novel synthetic pathway yielded a high-purity product which enabled determination of the crystal structure and magnetic properties of this compound. The crystal structure of Na₂AgF₄ contains infinite [AgF_2+4/2]²⁻ chains, in analogy to β-K₂AgF₄, but with a different packing of chains. The unusually short Ag²⁺Ag²⁺ contact of 3.342 Å within the chain is the shortest Ag²⁺Ag²⁺ distance among all structurally characterized compounds of divalent silver. This structural feature is responsible for the 1D antiferromagnetic properties of Na₂AgF₄ as determined from powder magnetic susceptibility measurements. These findings are rationalized with the aid of calculations of magnetic coupling constants within the framework of the Density Functional Theory including on-site Coulomb repulsion (DFT+U).