FR0s are compact radio sources that represent the bulk of the Radio-Loud (RL) AGN population, but they are still poorly understood. Pilot studies on these sources have been already performed at radio and optical wavelengths: here we present the first Xray study of a sample of 19 FR0 radio galaxies selected from the SDSS/NVSS/FIRST sample of Best & Heckman (2012), with redshift ≤ 0.15, radio size ≤ 10 kpc and optically classified as low-excitation galaxies (LEG). The X-ray spectra are modeled with a power-law component absorbed by Galactic column density with, in some cases, a contribution from thermal extended gas. The X-ray photons are likely produced by the jet as attested by the observed correlation between X-ray (2-10 keV) and radio (5 GHz) luminosities, similar to FRIs. The estimated Eddington-scaled luminosities indicate a low accretion rate. Overall, we find that the X-ray properties of FR0s are indistinguishable from those of FRIs, thus adding another similarity between AGN associated with compact and extended radio sources. A comparison between FR0s and low luminosity BL Lacs, rules out important beaming effects in the X-ray emission of the compact radio galaxies. FR0s have different X-ray properties with respect to young radio sources (e.g. GPS/CSS sources), generally characterized by higher X-ray luminosities and more complex spectra. In conclusion, the paucity of extended radio emission in FR0s is probably related to the intrinsic properties of their jets that prevent the formation of extended structures, and/or to intermittent activity of their engines.