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One-dimensional (1D) van der Waals (vdW) materials display electronic and magnetic transport properties that make them uniquely suited as interconnect materials and for low-dimensional optoelectronic applications. However, there are only around 700 1D vdW structures in general materials databases, making database curation approaches ineffective for 1D discovery. Here, we utilize machine-learning techniques to discover 1D vdW compositions that have not yet been synthesized. Our techniques go beyond discovery efforts involving elemental substitutions and instead start with a composition space of 4741 binary and 392,342 ternary formulas. We predict up to 3000 binary and 10,000 ternary 1D compounds and further classify them by expected magnetic and electronic properties. Our model identifies MoI3, a material we experimentally confirm to exist with wire-like subcomponents and exotic magnetic properties. More broadly, we find several chalcogen-, halogen-, and pnictogen-containing compounds expected to be synthesizable using chemical vapor deposition and chemical vapor transport.