  Primordial Black Holes (PBH) arise naturally from high peaks in the curvature
power spectrum of near-inflection-point single-field inflation, and could
constitute today the dominant component of the dark matter in the universe. In
this letter we explore the possibility that a broad spectrum of PBH is formed
in models of Critical Higgs Inflation (CHI), where the near-inflection point is
related to the critical value of the RGE running of both the Higgs
self-coupling $\lambda(\mu)$ and its non-minimal coupling to gravity
$\xi(\mu)$. We show that, for a wide range of model parameters, a
half-domed-shaped peak in the matter spectrum arises at sufficiently small
scales that it passes all the constraints from large scale structure
observations. The predicted cosmic microwave background spectrum at large
scales is in agreement with Planck 2015 data, and has a relatively large
tensor-to-scalar ratio that may soon be detected by B-mode polarization
experiments. Moreover, the wide peak in the power spectrum gives an
approximately lognormal PBH distribution in the range of masses $0.01 -
100\,M_\odot$, which could explain the LIGO merger events, while passing all
present PBH observational constraints. The stochastic background of
gravitational waves coming from the unresolved black-hole-binary mergers could
also be detected by LISA or PTA. Furthermore, the parameters of the CHI model
are consistent, within $2\sigma$, with the measured Higgs parameters at the LHC
and their running. Future measurements of the PBH mass spectrum could allow us
to obtain complementary information about the Higgs couplings at energies well
above the EW scale, and thus constrain new physics beyond the Standard Model.
