ABSTRACT In this paper we present a thorough discussion about the photometric redshift (photo-z) performance of the Southern Photometric Local Universe Survey (S-PLUS). This survey combines a seven narrow +5 broad passband filter system, with a typical photometric-depth of r ∼ 21 AB. For this exercise, we utilize the Data Release 1 (DR1), corresponding to 336 deg2 from the Stripe-82 region. We rely on the BPZ2 code to compute our estimates, using a new library of SED models, which includes additional templates for quiescent galaxies. When compared to a spectroscopic redshift control sample of ∼100 k galaxies, we find a precision of σz <0.8 per cent, <2.0 per cent, or <3.0 per cent for galaxies with magnitudes r < 17, <19, and <21, respectively. A precision of 0.6 per cent is attained for galaxies with the highest Odds values. These estimates have a negligible bias and a fraction of catastrophic outliers inferior to 1 per cent. We identify a redshift window (i.e. 0.26 < z < 0.32) where our estimates double their precision, due to the simultaneous detection of two emission lines in two distinct narrow bands; representing a window opportunity to conduct statistical studies such as luminosity functions. We forecast a total of ∼2 M, ∼16 M and ∼32 M galaxies in the S-PLUS survey with a photo-z precision of σz <1.0 per cent, <2.0 per cent, and <2.5 per cent after observing 8000 deg2. We also derive redshift probability density functions, proving their reliability encoding redshift uncertainties and their potential recovering the n(z) of galaxies at z < 0.4, with an unprecedented precision for a photometric survey in the Southern hemisphere.