  We investigate the critical behavior of three-dimensional relativistic
fermion models with a U(N_L)_L x U(1)_R chiral symmetry reminiscent of the
Higgs-Yukawa sector of the standard model of particle physics. We classify all
possible four-fermion interaction terms and the corresponding discrete
symmetries. For sufficiently strong correlations in a scalar parity-conserving
channel, the system can undergo a second-order phase transition to a
chiral-symmetry broken phase which is a 3d analog of the electroweak phase
transition. We determine the critical behavior of this phase transition in
terms of the critical exponent $\nu$ and the fermion and scalar anomalous
dimensions for N_L >= 1. Our models define new universality classes that can
serve as prototypes for studies of strongly correlated chiral fermions.
