Organic diradicals are highly promising candidates as future components in molecular electronic and spintronic devices because of their low spin-orbit coupling. To advance toward final circuit realizations, a thorough knowledge of the behavior of diradicals within a single-molecule junction framework is imperative. In this work, we have measured for the first time the single-molecule conductance of a neutral open-shell diradical compound, a [2,1-b] isomer of indenofluorene (IF). Our results reveal that the conductance of the [2,1-b] isomer is about 1 order of magnitude higher than that of the corresponding closed-shell regioisomer [1,2-b] IF. This is significant, as it fundamentally demonstrates the possibility of forming stable single-molecule junctions using neutral diradical compounds which are also highly conducting. This opens up a new approach to the development of externally addressable spintronic devices operable at room temperature.