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 on the [ Fe/H ] scale of Carretta & Gratton , as well as on a scale tied to the global metal abundance , [ M/H ] . The metallicity distribution function for red giant branch ( RGB ) stars in Leo I is confirmed to be very narrow , with mean value [ M/H ] \simeq - 1.2 and dispersion \sigma _ { [ M / H ] } \simeq 0.2 . By evaluating all contributions to the measurement error , we provide a constraint to the intrinsic metallicity dispersion , \sigma _ { [ M / H ] , 0 } = 0.08 . 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 \sim 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 .