In my talk I will show that production of the Higgs boson through gluon-fusion may be suppressed in the presence of colored scalars. Substantial destructive interference between the top quark diagrams and colored scalar diagrams is possible due to cancellations between the real (and also imaginary) parts of the amplitudes. As an example, I consider a color-octet scalar that has a negative, order one coupling to the Higgs doublet. As a result gluon fusion can be suppressed by more than an order of magnitude when the scalar mass is below a few hundred GeV, while milder suppressions occur for larger scalar masses or smaller couplings. Thus, the Standard Model extended with only one particle can evade the full range of present LHC exclusion limits on the Higgs mass. The colored scalars, however, would be produced in pairs with a large rate at the LHC, leading to multi-jet final states to which the LHC experiments are now becoming sensitive.