The theory of currents provides a powerful framework for studying geometric and variational problems where classical oriented surfaces are insufficient. Metric currents generalize this theory to spaces lacking a smooth manifold structure. A central open question in this setting is the Flat Chain Conjecture (FCC), which asserts that the space of metric currents coincides with the closure (in the mass norm) of all normal currents. While the FCC has been resolved for 1-dimensional and top-dimensional cases in Euclidean space, it has remained elusive in the general metric setting. In this talk, I will present a new approach via optimal transport that resolves the FCC for 1-dimensional currents in general metric spaces. This framework allows us to establish a Smirnov-type decomposition for 1-dimensional metric currents into SBV curves, providing a sharp structural description of these objects. This is joint work with Guy Bouchitté from IMath Toulon.