  We present the results of the first X-ray study of a sample of 16 young radio
sources classified as Compact Symmetric Objects (CSOs). We observed six of them
for the first time in X-rays using {\it Chandra}, re-observed four with the
previous {\it XMM-Newton} or {\it Beppo-SAX} data, and included six other with
the archival data. All the sources are nearby, $z<1$ with the age of their
radio structures ($<3000$~years) derived from the hotspots advance velocity.
Our results show heterogeneous nature of the CSOs indicating a complex
environment associated with young radio sources. The sample covers a range in
X-ray luminosity, $L_{2-10\,\rm keV} \sim 10^{41}$-$10^{45}$\,erg\,s$^{-1}$,
and intrinsic absorbing column density of $N_H \simeq
10^{21}$--10$^{22}$\,cm$^{-2}$. In particular, we detected extended X-ray
emission in 1718$-$649; a hard photon index of $\Gamma \simeq 1$ in 2021$+$614
and 1511$+$0518 consistent with either a Compton thick absorber or non-thermal
emission from compact radio lobes, and in 0710$+$439 an ionized iron emission
line at $E_{rest}=(6.62\pm0.04)$\,keV and EW $\sim 0.15-$1.4\,keV, and a
decrease by an order of magnitude in the 2-10 keV flux since the 2008 {\it
XMM-Newton} observation in 1607$+$26. We conclude that our pilot study of CSOs
provides a variety of exceptional diagnostics and highlights the importance of
deep X-ray observations of large samples of young sources. This is necessary in
order to constrain theoretical models for the earliest stage of radio source
evolution and study the interactions of young radio sources with the
interstellar environment of their host galaxies.
