We present the spectroscopy of red giant stars in the dwarf spheroidal galaxy Leo I, aimed at further constraining its chemical enrichment history. Intermediate-resolution spectroscopy in the Ca ii triplet spectral region was obtained for 54 stars in Leo I using FORS2 at the ESO Very Large Telescope. The equivalent widths of Ca ii triplet lines were used to derive the metallicities of the target stars We find a few metal-poor stars (whose metallicity values depend on the adopted extrapolation of the existing calibrations), but in no case are stars more metal-poor than [Fe/H] = −2.6. Our measurements provide a hint of a shallow metallicity gradient of −0.27 dex Kpc −1 among Leo I red giants. The gradient disappears if our data are combined with previous spectroscopic datasets in the literature, so that any firm conclusions about its presence must await new data, particularly in the outer regions. By combining the metallicities of the target stars with their photometric data, we provide age estimates and an age-metallicity relation for a subset of red giant stars in Leo I. Our age estimates indicate a rapid initial enrichment, a slowly rising metal abundance -consistent with the narrowness of the metallicity distribution -and an increase of ∼0.2 dex in the last few Gyr. The estimated ages also suggest a radial age gradient in the RGB stellar populations, which agrees with the conclusions of a parallel study of asymptotic giant branch stars in Leo I from near-infrared photometry. Together, these studies provide the first evidence of stellar population gradients in Leo I.