Context : Very old halo stars have previously been found to show at least four different abundance anomalies , which models of fast-rotating massive stars ( spinstars ) can successfully account for : rise of N/O and C/O , low ^ { 12 } C/ ^ { 13 } C , and a primary-like evolution of Be and B . Here we show the impact of these same stars in the enrichment of Sr and Ba in the early Universe . Aims : We study whether the s-process production of fast-rotating massive stars can offer an explanation for the observed spread in [ Sr/Ba ] ratio in halo stars with metallicity [ Fe/H ] < - 2.5 . Methods : By means of a chemical inhomogeneous model , we computed the enrichment of Sr and Ba by massive stars in the Galactic halo . Our model takes , for the first time , the contribution of spinstars into account . Results : The model ( combining an r-process contribution with an s-process from fast-rotating massive stars ) is able to reproduce the observed scatter in the [ Sr/Ba ] ratio at [ Fe/H ] < -2.5 . Toward higher metallicities , the stochasticity of the star formation fades away owing to the increasing number of exploding and enriching stars , and as a consequence the predicted scatter decreases . Conclusions : Our scenario is again based on the existence of spinstars in the early Universe . Very old halo stars have previously been found to show at least four other abundance anomalies , which rotating models of massive stars can successfully account for . Our results provide a fifth independent signature of fast-rotating massive stars : an early enrichment of the Universe in s-process elements .