  In chiral effective field theory the leading order (LO) nucleon-nucleon
potential includes two contact terms, in the two spin channels $S=0,1$, and the
one-pion-exchange potential. When the pion degrees of freedom are integrated
out, as in the pionless effective field theory, the LO potential includes two
contact terms only. In the three-nucleon system, the pionless theory includes a
three-nucleon contact term interaction at LO whereas the chiral effective
theory does not. Accordingly arbitrary differences could be observed in the LO
description of three- and four-nucleon binding energies. We analyze the two
theories at LO and conclude that a three-nucleon contact term is necessary at
this order in both theories. In turn this implies that subleading three-nucleon
contact terms should be promoted to lower orders. Furthermore this analysis
shows that one single low energy constant might be sufficient to explain the
large values of the singlet and triplet scattering lengths.
