Quasi-one-dimensional (quasi-1D) materials, with electron motion confined to linear chains, form an attractive set of compounds to study the physical properties in low dimensions. In this work, we report the observation of superconductivity and weak ferromagnetism in the noncentrosymmetric phase of the quasi-1D ${\left({\mathrm{TaSe}}_4\right)}_3\mathrm{I}$ single crystal. The superconductivity is probed by both the resistive transition and the Meissner effect below 2.5 K, while the ferromagnetic transition appears at $\sim 9$ K. Furthermore, the current-voltage data exhibit phase slip events, a typical characteristic of low-dimensional superconductors. Although a definite mechanism is difficult to pinpoint, first-principles calculations-based theoretical study suggests that Se dimer vacancies may give rise to this unusual ground state, simultaneously hosting these two antagonistic quantum phases. The present results provide a platform to study complex ground states of such quasi-1D materials.

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• Ferromagnetism
• Magnetism
• Superconductivity
• 1-dimensional systems