  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 7 narrow + 5 broad passband filter system,
with a typical photometric-depth of r$\sim$21 AB. For this exercise, we utilize
the Data Release 1 (DR1), corresponding to 336 deg$^{2}$ from the Stripe-82
region. We rely on the \texttt{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
$\sim$100k galaxies, we find a precision of $\sigma_{z}<$0.8\%, $<$2.0\% or
$<$3.0\% for galaxies with magnitudes r$<$17, $<$19 and $<$21, respectively. A
precision of 0.6\% is attained for galaxies with the highest \texttt{Odds}
values. These estimates have a negligible bias and a fraction of catastrophic
outliers inferior to 1\%. We identify a redshift window (i.e., 0.26$<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 $\sim$2M, $\sim$16M and $\sim$32M galaxies in the S-PLUS
survey with a photo-z precision of $\sigma_{z}<$1.0\%, $<$2.0\% and $<$2.5\%
after observing 8000 $deg^{2}$. 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.
