  We propose that inflation is driven by a (complex) neutral Higgs of the MSSM
extension of the SM, in a chaotic-like inflation setting. The SUSY breaking
soft term masses are of order $10^{12}-10^{13}$ GeV, which is identified with
the inflaton mass scale and is just enough to stabilise the SM Higgs potential.
The fine-tuned SM Higgs has then a mass around 126 GeV, in agreement with LHC
results. We point out that the required large field excursions of chaotic
inflation may be realised in string theory with the (complex) inflaton/Higgs
identified with a continuous Wilson line or D-brane position. We show specific
examples and study in detail a IIB orientifold with D7-branes at singularities,
with SM gauge group and MSSM Higgs sector. In this case the inflaton/Higgs
fields correspond to D7-brane positions along a two-torus transverse to them.
Masses and monodromy are induced by closed string $G_3$ fluxes, and the
inflaton potential can be computed directly from the DBI+CS action. We show how
this action sums over Planck suppressed corrections, which amount to a field
dependent rescaling of the inflaton fields, leading to a linear potential in
the large field regime. We study the evolution of the two components of the
Higgs/inflaton and compute the slow-roll parameters for purely adiabatic
perturbations. For large regions of initial conditions slow roll inflation
occurs and 50-60 efolds are obtained with r>0.07, testable in forthcoming
experiments. Our scheme is economical in the sense that both EWSB and inflation
originate in the same sector of the theory, all inflaton couplings are known
and reheating occurs efficiently.
