The chirally-odd twist-3 parton distribution function e^a(x) of the nucleon is studied in the large-N_c limit in the framework of the chiral quark-soliton model. It is demonstrated that in spite of properties not shared by other distribution functions, namely the appearance of a \delta (x)-singularity and quadratic divergences in e^a(x), an equally reliable calculation is possible. Among the most remarkable results obtained in this work is the fact that the coefficient of the \delta (x)-singularity can be computed exactly in this model, avoiding involved numerics. Our results complete existing studies in literature.

PACS numbers: 12.39.Fe, 11.15.Pg, 12.38.Lg, 13.60.Hb