  In the limit of many fermion flavors it is demonstrated that the sextic
Gross-Neveu theory in three dimensions displays a line of interacting UV fixed
points, characterised by an exactly marginal sextic interaction. We determine
the conformal window of UV-complete theories, universal scaling dimensions, and
the phase diagram using renormalisation group methods. Massless theories arise
naturally, and the generation of mass proceeds without the breaking of a
discrete symmetry. Striking similarities with critical scalar theories at large
$N$ are highlighted, and implications from the viewpoint of conformal field
theory and the AdS/CFT conjecture are indicated.
