High-quality epitaxial films of layered cobaltite Na_0.83CoO₂ were successfully grown on (0001)-oriented alpha-Al₂O₃ substrate by reactive solid-phase epitaxy using CoO epitaxial layer and NaHCO₃ powder. Thermal oxidation of the CoO film into Co₃O₄ occurs at lower temperature (300 ~ 500 ^oC). Then, Na_xCoO₂ epitaxial layer forms via lateral diffusion of Na⁺ ions together with oxide ions into Co₃O₄ layers, which take place at 600 ~ 700 ^oC. Epitaxial relationship between Na_0.83CoO₂ and alpha-Al₂O₃ were (0001)[11-20] Na_0.83CoO₂ || (0001)[1-100] alpha-Al₂O₃. Thermoelectric properties such as electrical conductivity (sigma), carrier hole concentration, Hall mobility and Seebeck coefficient (S), and power factor (S²sigma) of Na_xCoO₂ epitaxial layer were 1,160 Scm^-1, 3.8 x 10²¹ cm^-3, 1.9 cm²V^-1s^-1, +117 microVK^-1, and 1.6 x 10^-3 Wm^-1K^-2, respectively, which were comparable to those of bulk single-crystalline Na_xCoO₂.