We report the first spectroscopic detection of a kink MHD oscillation of a solar coronal structure by the Extreme-Ultraviolet Imaging Spectrometer (EIS) on the Japanese Hinode satellite. The detected oscillation has an amplitude of 1 km s-1 in the Doppler shift of the FeXII 195 Å spectral line (1.3~MK), and a period of 296~s. The unique combination of EIS's spectroscopic and imaging abilities enables us to measure simultaneously the mass density and length of the oscillating loop. This enables us to measure directly the magnitude of the local magnetic field, the fundamental coronal plasma parameter, as 39 ± 8~G, with unprecedented accuracy. This proof of concept makes EIS an exclusive instrument for the full scale implementation of the MHD coronal seismological technique.