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.
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