We investigate the possibility of using the ratio between the 2–10 keV flux and the Ne V3426 emission line flux (X/NeV) as a diagnostic diagram to discover heavily obscured, possibly Compton-thick active galactic nuclei (AGN) in the distant Universe. While it is on average about one order of magnitude fainter than the more commonly used O III5007 emission line, the Ne V3426 line can be observed with optical spectroscopy up to z~1.5, whereas the O III5007 line is redshifted out of the optical bands already at z~0.8. First, we calibrated a relation between X/NeV and the cold absorbing column density NH using a sample of 74 bright, nearby Seyferts with both X-ray and Ne V data available in the literature and for which the column density is determined unambiguously. Similar to what is found for the X-ray to O III5007 flux ratio (X/OIII), we found that the X/NeV ratio decreases towards high column densities, as expected if Ne V3426 emission is a good tracer of the AGN intrinsic power. Essentially all local Seyferts with X/NeV values below 15 are found to be Compton-thick objects. At X/NeV values below 100, the percentage of Compton-thick nuclei decreases to ~50%, but ~80% of the considered sample is still absorbed with NH > 1023 cm-2. Second, we applied this diagnostic diagram to different samples of distant obscured and unobscured QSOs in the Sloan Digital Sky Survey (SDSS). SDSS blue, unobscured, type-1 QSOs in the redshift range z = 0.1–1.5 indeed show X/NeV values typical of unobscured Seyfert 1s in the local Universe. Conversely, SDSS type-2 QSOs at z~0.5 classified either as Compton-thick or Compton-thin on the basis of their X/OIII ratio, would have mostly been classified in the same way based on the X/NeV ratio. We applied the X/NeV diagnostic diagram to 9 SDSS obscured QSOs in the redshift range z = 0.85–1.31, selected by means of their prominent Ne V3426 line (rest EW > 4 Å) and observed with Chandra ACIS-S for 10ks each (8 of them as part of our proprietary program). Based on the X/NeV ratio, complemented by X-ray spectral analysis, 2 objects appear good Compton-thick QSO candidates, 4 objects appear as Compton-thin QSOs, while 3 have an ambiguous classification. When excluding broad-lined QSOs with a red continuum from the sample and thus considering only genuine narrow-line objects, the efficiency in selecting Compton-thick QSOs through the Ne V line is about 50% (with large errors, though), more similar to what is achieved with O III selection. We discuss the possibility of applying the X/NeV diagnostic to deep X-ray surveys to search for Compton-thick Seyferts at z~1, i.e., those objects that are thought to be responsible for the “missing” X-ray background. Finally, we compared the optical spectral properties of Ne V-selected QSOs with those of other SDSS populations of obscured and unobscured QSOs. By restricting the analysis to objects in the same redshift (and luminosity) range z = 0.4–1.5, we found evidence that, at any given Ne V luminosity, increasing obscuration is accompanied by increasing O II3727 emission. This correlation is interpreted as evidence of enhanced star formation in obscured QSOs, which is consistent with current popular scenarios of BH-galaxy coevolution.