  We report the detection of a dark substructure through direct gravitational
imaging - undetected in the HST-ACS F814W image - in the gravitational lens
galaxy of SLACS SDSSJ0946+1006 (the "Double Einstein Ring"). The detection is
based on a Bayesian grid reconstruction of the two-dimensional surface density
of the galaxy inside an annulus around its Einstein radius (few kpc). [...] We
confirm this detection by modeling the system including a parametric mass model
with a tidally truncated pseudo-Jaffe density profile; in that case the
substructure mass is M_sub=(3.51+-0.15)x10^9 Msun, located at
(-0.651+-0.038,1.040+-0.034)'', precisely where also the surface density map
shows a strong convergence peak. [...] We set a lower limit of (M/L)_V}>=120
(Msun/L}_V,sun (3-sigma) inside a sphere of 0.3 kpc centred on the substructure
(r_tidal=1.1kpc). The result is robust under substantial changes in the model
and the data-set (e.g. PSF, pixel number and scale, source and potential
regularization, rotations and galaxy subtraction). Despite being at the limits
of detectability, it can therefore not be attributed to obvious systematic
effects. Our detection implies a dark matter mass fraction at the radius of the
inner Einstein ring of f_CDM=2.15^{+2.05}_{-1.25} percent (68 percent C.L) in
the mass range 4x10^6 Msun to 4x10^9 Msun assuming alpha=1.9+-0.1 (with dN/dm ~
m^-alpha). Assuming a flat prior on alpha, between 1.0 and 3.0, increases this
to f_CDM=2.56^{+3.26}_{-1.50} percent (68 percent C.L). The likelihood ratio is
0.51 between our best value (f_CDM=0.0215) and that from simulations
(f_sim=0.003). Hence the inferred mass fraction, admittedly based on a single
lens system, is large but still consistent with predictions. [...]
