  We study the importance of few-nucleon forces in chiral effective field
theory for describing many-nucleon systems. A combinatorial argument suggests
that three-nucleon forces -- which are conventionally regarded as
next-to-next-to-leading order -- should accompany the two-nucleon force already
at leading order (LO) starting with mass number $A\approx 10-20$. We find that
this promotion enables the first realistic description of the $^{16}$O ground
state based on a renormalization-group-invariant LO interaction. We also
performed coupled-cluster calculations of the equation of state for symmetric
nuclear matter and our results indicate that LO four-nucleon forces could play
a crucial role for describing heavy-mass nuclei. The enhancement mechanism we
found is very general and could be important also in other many-body problems.
