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(Abridged) We present the spectroscopy of red giant stars in the dwarfspheroidal galaxy LeoI, aimed at further constraining its chemical enrichmenthistory. Intermediate-resolution spectroscopy in the CaII triplet spectralregion was obtained for 54 stars in LeoI using FORS2 at the ESO Very LargeTelescope. The equivalent widths of CaII triplet lines were used to derive themetallicities of the target stars on the [Fe/H] scale of Carretta & Gratton, aswell as on a scale tied to the global metal abundance, [M/H].  The metallicity distribution function for LeoI stars is confirmed to be verynarrow, with mean value [M/H]~-1.2 and intrinsic dispersion, sigma_[M/H]=0.08.We find a few metal-poor stars (whose metallicity values depend on the adoptedextrapolation of the existing calibrations), but in no case are stars moremetal-poor than [Fe/H]=-2.6.  Our measurements provide a hint of a shallow metallicity gradient of -0.27dex/Kpc among LeoI red giants.  By combining the metallicities of the target stars with their photometricdata, we provide age estimates and an age-metallicity relation for a subset ofred giant stars in LeoI. Our age estimates indicate a rapid initial enrichment,a slowly rising metal abundance and an increase of ~0.2 dex in the last fewGyr.

New constraints on the chemical evolution of the dwarf spheroidal galaxy LeoI from VLT spectroscopy