  We study a two-parameter extension of the cosmological standard model
$\Lambda$CDM in which cold dark matter interacts with a new form of dark
radiation. The two parameters correspond to the energy density in the dark
radiation fluid $\Delta N_\mathrm{fluid}$ and the interaction strength between
dark matter and dark radiation. The interactions give rise to a very weak "dark
matter drag" which damps the growth of matter density perturbations throughout
radiation domination, allowing to reconcile the tension between predictions of
large scale structure from the CMB and direct measurements of $\sigma_8$. We
perform a precision fit to Planck CMB data, BAO, large scale structure, and
direct measurements of the expansion rate of the universe today. Our model
lowers the $\chi$-squared relative to $\Lambda$CDM by about 12, corresponding
to a preference for non-zero dark matter drag by more than $3 \sigma$. Particle
physics models which naturally produce a dark matter drag of the required form
include the recently proposed non-Abelian dark matter model in which the dark
radiation corresponds to massless dark gluons.
