A heavy Standard Model Higgs boson is not only disfavored by electroweak precision observables but is also excluded by direct searches at the 7 TeV LHC for a wide range of masses. Here, we examine scenarios where a heavy Higgs boson can be made consistent with both the indirect constraints and the direct null searches by adding only one new particle beyond the Standard Model. This new particle should be a weak multiplet in order to have additional contributions to the oblique parameters. If it is a color singlet, we find that a heavy Higgs with an intermediate mass of 200 - 300 GeV can decay into the new states, suppressing the branching ratios for the standard model modes, and thus hiding a heavy Higgs at the LHC. If the new particle is also charged under QCD, the Higgs production cross section from gluon fusion can be reduced significantly due to the new colored particle one-loop contribution. Current collider constraints on the new particles allow for viable parameter space to exist in order to hide a heavy Higgs boson. We categorize the general signatures of these new particles, identify favored regions of their parameter space and point out that discovering or excluding them at the LHC can provide important indirect information for a heavy Higgs. Finally, for a very heavy Higgs boson, beyond the search limit at the 7 TeV LHC, we discuss three additional scenarios where models would be consistent with electroweak precision tests: including an additional vector-like fermion mixing with the top quark, adding another U(1) gauge boson and modifying triple-gauge boson couplings. Show Partial Abstract