  We present a non-perturbative determination of the upper and lower Higgs
boson mass bounds with a heavy fourth generation of quarks from numerical
lattice computations in a chirally symmetric Higgs-Yukawa model. We find that
the upper bound only moderately rises with the quark mass while the lower bound
increases significantly, providing additional constraints on the existence of a
straight-forward fourth quark generation. We examine the stability of the lower
bound under the addition of a higher dimensional operator to the scalar field
potential using perturbation theory, demonstrating that it is not significantly
altered for small values of the coupling of this operator. For a Higgs boson
mass of $\sim125\mathrm{GeV}$ we find that the maximum value of the fourth
generation quark mass is $\sim300\mathrm{GeV}$, which is already in conflict
with bounds from direct searches.
