ATLAS and CMS have each reported a modest diphoton excess consistent with the
decay of a broad resonance at ~ 750 GeV. We show how this signal can arise in a
weakly coupled theory comprised solely of narrow width particles. In
particular, if the decaying particle is produced off-shell, then the associated
diphoton resonance will have a broad, adjustable width. We present simplified
models which explain the diphoton excess through the three-body decay of a
scalar or fermion. Our minimal ultraviolet completion is a weakly coupled and
renormalizable theory of a singlet scalar plus a heavy vector-like quark and
lepton. The smoking gun of this mechanism is an asymmetric diphoton peak
recoiling against missing transverse energy, jets, or leptons
