  Green Peas represent a population of compact, highly star-forming dwarf
galaxies at redshifts z ~ 0.2-0.3 that have recently been found to show
signatures of ultraviolet ionizing radiation leakage. They are being considered
as analogs to high-redshift star-forming galaxies, possibly responsible for the
cosmic reionization. Despite the intensive studies of Green Peas in the
ultraviolet and optical domains, their X-ray properties have only so far been
probed by nearby analogs. In this paper, we present the first measurements of
Green Peas in the X-ray domain to constrain their spectral properties and
fluxes at high energies. We analyzed XMM-Newton observations of three Green Pea
sources. For two of them, we found an X-ray luminosity exceeding by a
half-order of magnitude its predicted value, derived from the star formation
rate and metallicity. Only an upper limit of the X-ray luminosity was derived
for the third studied galaxy. Our results thus indicate that at least some
Green Peas produce copious amounts of highly energetic photons, larger than
detected in other star-forming galaxies. We discuss possible physical scenarios
for the measured X-ray excess, including the presence of a hidden active
galactic nucleus, a larger population of X-ray binaries, or ultra-luminous
X-ray sources. Future spatially resolved X-ray images will discriminate between
the models. Larger Green Pea samples will provide a possible link between the
X-ray properties and the leaking ultraviolet radiation.

Astrophysics of Galaxies