  We present a multi-epoch, multi-observatory X-ray analysis for 2FHL
J1745.1-3035, a newly discovered very high energy Galactic source detected by
the Fermi Large Area Telescope (LAT) located in close proximity to the Galactic
Center (l=358.5319{\deg}; b=-0.7760{\deg}). The source shows a very hard
gamma-ray photon index above 50 GeV, Gamma_gamma=1.2+-0.4, and is found to be a
TeV-emitter by the LAT. We conduct a joint XMM-Newton, Chandra and NuSTAR
observing campaign, combining archival XMM-Newton observations, to study the
X-ray spectral properties of 2FHL J1745.1-3035 over a time-span of over 20
years. The joint X-ray spectrum is best-fitted as a broken power law model with
break energy E_b~7 keV: the source is very hard at energies below 10 keV, with
photon index Gamma_1~0.6, and significantly softer in the higher energy range
measured by NuSTAR with photon index Gamma_2~1.9. We also perform a spatially
resolved X-ray analysis with Chandra, finding evidence for marginal extension
(up to an angular size r~5 arcsec), a result that supports a compact pulsar
wind nebula scenario. Based on the X-ray and gamma-ray properties, 2FHL
J1745.1-3035 is a powerful pulsar wind nebula candidate. Given its nature as an
extreme TeV emitter, further supported by the detection of a coincident TeV
extended source HESS J1745-303, 2FHL J1745.1-3035 is an ideal candidate for a
follow-up with the upcoming Cherenkov Telescope Array.
