We investigate the singlet g(T)((0)) and isovector g(T)((3)) tensor ch
arges of the nucleon, which are deeply related to the first moment of
the leading twist transversity quark distribution h(1)(x), in the SU(2
) chiral quark-soliton model. With rotational O(1/N-c) corrections tak
en into account, we obtain g(T)((0))=0.69 and g(T)((3))=1.45 at a low
normalization point of several hundreds MeV. Within the same approxima
tion and parameters the model yields g(A)((0))=0.36, g(A)((3))=1.21 fo
r axial charges and a correct octet-decuplet mass splitting. We show h
ow the chiral quark-soliton model interpolates between the nonrelativi
stic quark model and the Skyrme model.