  The newly discovered resonance at 125 GeV has properties consistent with the
Standard Model (SM) Higgs particle, although some production and/or decay
channels currently exhibit O(1) deviations. We consider scenarios with a new
scalar singlet field with couplings to electrically charged vector-like matter,
focusing particularly on the case when the singlet mass lies within a narrow ~
few GeV window around the Higgs mass. Such a `singlet neighbor' presents novel
mechanisms for modifying the observed properties of the Higgs boson. For
instance, even a small amount of the Higgs-singlet mixing can lead to a
significant enhancement of the apparent diphoton rate. Alternatively, the Higgs
may decay into the nearby singlet, along with a very light, very soft mediator
particle, in which case there can be O(1) enhancement to the apparent diphoton
rate even for ~ TeV-scale charged vector-like matter. We also explore models in
which vector-like fermions mix with the SM leptons, causing the simultaneous
enhancement of diphoton and suppression of ditau Higgs branching ratios. Our
scenario can be tested with the accumulating LHC data by probing for the
diresonance structure of the 125 GeV diphoton signal, as well as the relative
shift in the resonance location between the diphoton and four-lepton modes.
