  A unitary transformation allows to remove redundant terms in the two-nucleon
(2N) contact interaction at the fourth order (N3LO) in the low-energy expansion
of Chiral Effective Field Theory. In so doing a three-nucleon (3N) interaction
is generated. We express its short-range component in terms of five
combinations of low-energy constants (LECs) parametrizing the N3LO 2N contact
Lagrangian. Within a hybrid approach, in which this interaction is considered
in conjunction with the phenomenological AV18 2N potential, we show that the
involved LECs can be used to fit very accurate data on polarization observables
of low-energy $p-d$ scattering, in particular the $A_y$ asymmetry. The
resulting interaction is of the right order of magnitude for a N3LO
contribution.
