  We extend the list of theories featuring a rigorous interacting ultraviolet
fixed point by constructing the first theory featuring a Higgs-like scalar with
gauge, Yukawa and quartic interactions. We show that the theory enters a
perturbative asymptotically safe regime at energies above a physical scale
$\Lambda$. We determine the salient properties of the theory and use it as a
concrete example to test whether scalars masses unavoidably receive quantum
correction of order $\Lambda$. Having at our dispose a calculable model
allowing us to precisely relate the IR and UV of the theory we demonstrate that
the scalars can be lighter than $\Lambda$. Although we do not have an answer to
whether the Standard Model hypercharge coupling growth towards a Landau pole at
around $\Lambda \sim 10^{40}$ GeV can be tamed by non-perturbative asymptotic
safety, our results indicate that such a possibility is worth exploring. In
fact, if successful, it might also offer an explanation for the unbearable
lightness of the Higgs.
