We report the first detailed chemical abundance analysis of the exoplanet-hosting M-dwarf stars Kepler-138 and Kepler-186 from the analysis of high-resolution (R~22,500) H-band spectra from the SDSS IV - APOGEE survey. Chemical abundances of thirteen elements - C, O, Na, Mg, Al, Si, K, Ca, Ti, V, Cr, Mn, and Fe - are extracted from the APOGEE spectra of these early M-dwarfs via spectrum syntheses computed with an improved line list that takes into account H2O and FeH lines. This paper demonstrates that APOGEE spectra can be analyzed to determine detailed chemical compositions of M-dwarfs. Both exoplanet-hosting M-dwarfs display modest sub-solar metallicities: [Fe/H]_Kepler-138 = -0.09+-0.09 dex and [Fe/H]_Kepler-186 = -0.08+-0.10 dex. The measured metallicities resulting from this high-resolution analysis are found to be higher by ~0.1-0.2 dex than previous estimates from lower-resolution spectra. The C/O ratios obtained for the two planet-hosting stars are near-solar, with values of 0.55+-0.10 for Kepler-138 and 0.52+-0.12 for Kepler-186. Kepler-186 exhibits a marginally enhanced [Si/Fe] ratio.