At large N-c the nucleon can be viewed as a soliton of the effective c
hiral lagrangian. This picture of nucleons allows for a consistent non
-perturbative calculation of the leading-twist parton distributions at
a low normalization point. We derive general formulae for the polariz
ed and unpolarized distributions (singlet and non-singlet) in the chir
al quark-soliton model. The consistency of our approach is demonstrate
d by checking the baryon number, isospin and total momentum sum rules,
as well as the Bjorken sum rule. We present numerical estimates of th
e quark and antiquark distributions and find reasonable agreement with
parameterizations of the data at a low normalization point. In partic
ular, we obtain a sizeable fraction of antiquarks, in agreement with t
he phenomenological analysis.