A fraction of active galactic nuclei do not show the classical Seyfert-type signatures in their optical spectra, i.e. they are optically "elusive". X-ray observations are an optimal tool to identify this class of objects. We combine new Chandra observations with archival X-ray data in order to obtain a first estimate of the fraction of elusive AGN in local galaxies and to constrain their nature. Our results suggest that elusive AGN have a local density comparable to or even higher than optically classified Seyfert nuclei. Most elusive AGN are heavily absorbed in the X-rays, with gas column densities exceeding 10^24 cm^-2, suggesting that their peculiar nature is associated with obscuration. It is likely that in elusive AGN, the nuclear UV source is completely embedded and the ionizing photons cannot escape, which prevents the formation of a classical Narrow Line Region. Elusive AGN may contribute significantly to the 30 keV bump of the X-ray background.

accepted for publication in MNRAS Letters, 6 pages, 3 figures, typos and references corrected