  We investigate chiral Higgs-Yukawa models with a non-abelian gauged
left-handed sector reminiscent to a sub-sector of the standard model. We
discover a new weak-coupling fixed-point behavior that allows for ultraviolet
complete RG trajectories which can be connected with a conventional long-range
infrared behavior in the Higgs phase. This non-trivial ultraviolet behavior is
characterized by asymptotic freedom in all interaction couplings, but a quasi
conformal behavior in all mass-like parameters. The stable microscopic scalar
potential asymptotically approaches flatness in the ultraviolet, however, with
a non-vanishing minimum increasing inversely proportional to the asymptotically
free gauge coupling. This gives rise to nonperturbative -- though weak-coupling
-- threshold effects which induce ultraviolet stability along a line of fixed
points. Despite the weak-coupling properties, the system exhibits non-Gaussian
features which are distinctly different from its standard perturbative
counterpart: e.g., on a branch of the line of fixed points, we find linear
instead of quadratically running renormalization constants. Whereas the Fermi
constant and the top mass are naturally of the same order of magnitude, our
model generically allows for light Higgs boson masses. Realistic mass ratios
are related to particular RG trajectories with a "walking" mid-momentum regime.
