The nature of metallicity and the level of electronic correlations in the antiferromagnetically ordered parent compounds are two important open issues for the iron-based superconductivity. We perform a temperature-dependent angle-resolved photoemission spectroscopy study of Fe(1.02)Te, the parent compound for iron chalcogenide superconductors. Deep in the antiferromagnetic state, the spectra exhibit a "peak-dip-hump" line shape associated with two clearly separate branches of dispersion, characteristics of polarons seen in manganites and lightly doped cuprates. As temperature increases towards the Néel temperature (T(N)), we observe a decreasing renormalization of the peak dispersion and a counterintuitive sharpening of the hump linewidth, suggestive of an intimate connection between the weakening electron-phonon (e-ph) coupling and antiferromagnetism. Our finding points to the highly correlated nature of the Fe(1.02)Te ground state featured by strong interactions among the charge, spin, and lattice and a good metallicity plausibly contributed by the coherent polaron motion.