We have used high-resolution spectra obtained with the multifiber facility FLAMES at the Very Large Telescope of the European Southern Observatory to derive kinematic properties and chemical abundances of Fe, O, Mg, and Si for 89 stars in the disk of the Large Magellanic Cloud (LMC). The derived metallicity and [{alpha}/Fe], obtained as the average of O, Mg, and Si abundances, allow us to draw a preliminary scheme of the star formation history of this region of the LMC. The derived metallicity distribution shows two main components: one component (comprising ~84% of the sample) peaks at [Fe/H]=-0.48dex and it shows an [{alpha}/Fe] ratio slightly under solar ([{alpha}/Fe]~-0.1dex). This population probably originated in the main star formation event that occurred 3-4Gyr ago (possibly triggered by tidal capture of the Small Magellanic Cloud). The other component (comprising ~16% of the sample) peaks at [Fe/H]~-0dex and it shows an [{alpha}/Fe]~0.2dex. This population was probably generated during the long quiescent epoch of star formation between the first episode and the most recent bursts. Indeed, in our sample we do not find stars with chemical properties similar to the old LMC globular clusters nor to the iron-rich and {alpha}-poor stars recently found in the LMC globular cluster NGC 1718 and also predicted to be in the LMC field, thus suggesting that both of these components are small (<1%) in the LMC disk population.