  We perform the first complete analysis of nd scattering at
next-to-next-to-leading order in chiral effective field theory including the
corresponding three-nucleon force and extending our previous work, where only
the two-nucleon interaction has been taken into account. The three-nucleon
force appears first at this order in the chiral expansion and depends on two
unknown parameters. These two parameters are determined from the triton binding
energy and the nd doublet scattering length. We find an improved description of
various scattering observables in relation to the next-to-leading order results
especially at moderate energies (E_lab = 65 MeV). It is demonstrated that the
long-standing A_y-problem in nd elastic scattering is still not solved by the
leading 3NF, although some visible improvement is observed. We discuss
possibilities of solving this puzzle. The predicted binding energy for the
alpha-particle agrees with the empirical value.
