Abstract 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; b = −0.°7760). The source shows a very hard γ-ray photon index above 50 GeV, Γ _γ = 1.2 ± 0.4, and is found to be a TeV emitter by the Fermi–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 yr. 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 Γ₁ ∼ 0.6, and significantly softer in the higher energy range measured by NuSTAR with Γ₂ ∼ 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″), a result that supports a compact pulsar wind nebula scenario. Based on the X-ray and γ-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.