We present JWST NIRSpec and MIRI observations of the metal-poor T dwarf WISEA J155349.96+693355.2. The combined NIRSpec/prism plus MIRI/LRS spectrum (R ~ 100) provides 0.6-12 μm spectroscopic coverage that reveals the presence of H₂O, CH₄, and NH₃ absorption features, enhanced collision-induced H₂ absorption, and weak or absent CO and CO₂ absorption, all indicators of a metal-poor low-temperature atmosphere. Comparison of the spectral data to a suite of atmosphere models yields an effective temperature T_(rm eff) = 960⁺²⁸₋₃₂ K and a solar-scaled metallicity of [M/H] = -1.16^(+0.28)_(-0.25) dex. We find indications that the uncertain trigonometric parallax, likely subject to Lutz-Kelker bias, may be overestimated. Adopting the photometric distance yields a bolometric luminosity log₁₀L_bol/L_⊙ = -5.29 ± 0.10, from which we infer T_(rm eff) = 974 ± 56 K, consistent with the temperature derived via our atmospheric model fits. From the moderate-resolution (R ~ 3,000) NIRSpec/G395H spectrum, we measure a radial velocity of -163 ± 5 km/s, which combined with the source's measured proper motion and estimated distance indicates a highly eccentric (e ≥ 0.9) Galactic orbit consistent with an accreted halo object. The UVW kinematics of WISEA J155349.96+693355.2, its bulk metallicity, and its modest alpha enrichment ([α/Fe] = +0.15^(+0.04)_(-0.06) dex) are all equivalent to stars identified in the Gaia-Enceladus Milky Way substructure, making it the first brown dwarf with kinematic and chemical evidence of association.