Quasi-one-dimensional (Q1D) systems are inherently unfavorable for superconductivity due to electronic instabilities and significant quantum fluctuations. This has led to a half-century-long pursuit of strong and robust Q1D superconductors. Herein, we propose an effective multiorbital chain approach that utilizes the interorbital self-doping to not only suppress the instability but also to position the Fermi level near the band edges. Crucially, the introduced multiorbital band crossings simultaneously create significant interband pairings that suppress pair fluctuations. As a result, strong and robust Q1D superconductivity becomes achievable. Our proposal is further realized in a realistic material system, namely, chainlike NaBe. Ab initio Eliashberg theory calculations predict a high superconducting transition temperature (${T}_{\mathrm{C}}$) of 17.2 K in NaBe, owing to its significant interband pairings and band-edge effects. Under doping or pressure, the ${T}_{\mathrm{C}}$ is boosted to over 20 K, which greatly exceeds the record of 11.5 K of all known Q1D superconductors. This work paves the way for discovering strong and robust Q1D superconductors in the multiorbital BCS-Eliashberg frame.