We have searched ~8200 sq. degs for high proper motion (~0.5-2.7/year) T dwarfs by combining first-epoch data from the Pan-STARRS1 (PS1) 3-Pi Survey, the 2MASS All-Sky Point Source Catalog, and the WISE Preliminary Data Release. We identified two high proper motion objects with the very red (W1-W2) colors characteristic of T dwarfs, one being the known T7.5 dwarf GJ 570D. Near-IR spectroscopy of the other object (PSO J043.5+02 = WISEP J0254+0223) reveals a spectral type of T8, leading to a photometric distance of 7.2+/-0.7 pc. The 2.56/yr proper motion of PSO J043.5+02 is the second highest among field T dwarfs, corresponding to an tangential velocity of 87+/-8 km/s. According to the Besancon galaxy model, this velocity indicates its galactic membership is probably in the thin disk, with the thick disk an unlikely possibility. Such membership is in accord with the near-IR spectrum, which points to a surface gravity (age) and metallicity typical of the field population. We combine 2MASS, SDSS, WISE, and PS1 astrometry to derive a preliminary parallax of 171+/-45 mas (5.8{+2.0}{-1.2} pc), the first such measurement using PS1 data. The proximity and brightness of PSO J043+02 will facilitate future characterization of its atmosphere, variability, multiplicity, distance, and kinematics. The modest number of candidates from our search suggests that the immediate (~10 pc) solar neighborhood does not contain a large reservoir of undiscovered T dwarfs earlier than about T8.
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