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Open‐shell materials bearing multiple spin centres provide a key route to efficient charge transport in single‐molecule electronic devices. They have narrow energy gaps, and their molecular orbitals align closely to the Fermi level of the metallic electrodes, thus allowing efficient electronic transport and higher conductance. Maintaining and stabilising multiple open‐shell states—especially in contact with metallic electrodes—is however very challenging, generally requiring a continuous chemical or electrochemical potential to avoid self‐immolation of the open‐shell character. To overcome this issue, we designed, synthesised, and measured the conductance of a series of bis(indeno) fused acenes, where stability is imparted by a close‐shell quinoidal conformation in resonance with the diradical electronic configuration. We show here that these compounds have anti‐ohmic behaviour, with conductance increasing with increasing molecular length, at an unprecedented rate and across the entire bias window (±1.3V ${\pm 1.3\ V}$). Density Functional Theory (DFT) calculations support our findings, showing the rapidly narrowing HOMO–LUMO gap, unique to these diradicaloid structures, is responsible for the observed behaviour. Our results provide a framework for achieving efficient transport in neutral compounds and demonstrate the promise that diradicaloid materials have in single‐molecule electronics, owing to their great stability and unique electronic structure. [ABSTRACT FROM AUTHOR] more...