Current LHC data indicate that H(125) is either the single Higgs of the Standard Model or, to a good approximation, an “aligned Higgs”. We propose that it is the pseudo-Goldstone dilaton of Gildener and Weinberg. This naturally and, we conjecture, uniquely accounts for its low mass and its alignment. It further implies the existence of additional Higgs bosons in the range ~200 to ~550 GeV. We illustrate this in a version of a 2HDM of Lee and Pilaftsis. Our version is consistent with all published precision EW (LEP) and LHC (ATLAS & CMS) data. We propose tests to confirm or exclude this model with available LHC data. These include surprising new results on di-Higgs production and related processes.