  The presence of an invisible substructure has previously been detected in the
gravitational lens galaxy SDSSJ0946+1006 through its perturbation of the lensed
images. Using flexible models for the main halo and the subhalo perturbation to
fit the lensed images, we demonstrate that the subhalo has an extraordinarily
high central density and steep density slope. The inferred concentration for
the subhalo is well above the expected scatter in concentrations for
$\Lambda$CDM halos of similar mass. We robustly infer the subhalo's projected
mass within 1 kpc to be $\sim 2$-$3.7\times 10^9$M$_\odot$ at $>$95% CL for all
our lens models, while the average slope of the subhalo's projected density
profile over the radial range 0.75-1.25 kpc is constrained to be steeper than
isothermal ($\gamma_{2D} \lesssim -1$). By modeling the subhalo light directly,
we infer a conservative upper bound on its luminosity $L_V < 1.2\times
10^8L_\odot$ at 95% CL, which shows that the perturber is dark matter
dominated. To compare to $\Lambda$CDM expectations, we analyze subhalos within
analogues of lensing galaxies in the Illustris TNG100-1 simulation over many
lines of sight, and find hundreds of subhalos that achieve a projected mass
within 1 kpc of $\gtrsim 2\times10^9M_\odot$. However, less than 1% of the mock
observations yield a log-slope steep enough to be consistent with our lensing
models, and they $all$ have stellar masses in excess of that allowed by
observations by about an order of magnitude or more. We conclude that the
presence of such a dark, highly concentrated subhalo is unexpected in a
$\Lambda$CDM universe. Finally, we show that this tension with CDM is not
significantly reduced if the perturber is assumed to be a line-of-sight
structure, rather than a subhalo.
