We present the metallicity distribution of a sample of 471 RR Lyrae (RRL) stars in the Sculptor dSph, obtained from the I-band period-luminosity relation. It is the first time that the early chemical evolution of a dwarf galaxy is characterized in such a detailed and quantitative way, using photometric data alone. We find a broad metallicity distribution (full width at half-maximum equals to 0.8 dex) that is peaked at [Fe/H] ≃ -1.90 dex, in excellent agreement with literature values obtained from spectroscopic data. Moreover, we are able to directly trace the metallicity gradient out to a radius of ˜55 arcmin. We find that in the outer regions (r >˜32 arcmin) the slope of the metallicity gradient from the RRLs (-0.025 dex arcmin-1) is comparable to the literature values based on red giant (RG) stars. However, in the central part of Sculptor, we do not observe the latter gradients. This suggests that there is a more metal-rich and/or younger population in Sculptor that does not produce RRLs. This scenario is strengthened by the observation of a metal-rich peak in the metallicity distribution of RG stars by other authors, which is not present in the metallicity distribution of the RRLs within the same central area.