In this paper we have studied the two-pion exchange three-nucleon potential
(2 pi E-3NP) using an approximate SU(2) x SU(2) chiral symmetry of the str
ong interaction. The off-shell pion-nucleon scattering amplitudes obtained
from the Weinberg Lagrangian are supplemented with contributions from the w
ell-known sigma-term and the Delta(1232) exchange. It is the role of the De
lta-resonance in 2 pi E - 3NP, which we have investigated in detail in the
framework of the Lagrangian field theory. The Delta-contribution is quite a
ppreciable and, more significantly, it is dependent on a parameter Z which
is arbitrary but has the empirical bounds \Z\ less than or equal to 1/2. We
find that the Delta-contribution to the important parameters of the 2 pi E
- 3NP depends on the choice of a value for Z, although the correction to t
he binding energy of triton is not expected to be very sensitive to the var
iation of Z within its bounds.