We entertain the possibility that neutrino masses and dark matter (DM) originate from a common composite dark sector. A minimal effective theory can be constructed based on a dark SU(3)D interaction with three flavors of massless dark quarks; electroweak symmetry breaking gives masses to the dark quarks. By assigning a Z2 charge to one flavor, a stable “dark kaon” can provide a good thermal relic DM candidate. We find that “dark neutrons” may be identified as right handed Dirac neutrinos. Some level of “neutron-anti-neutron” oscillation in the dark sector can then result in non-zero Majorana masses for light standard model neutrinos. A simple ultraviolet completion is presented, involving additional heavy SU(3)D-charged particles with electroweak and lepton Yukawa couplings. At our benchmark point, there are “dark pions” that are much lighter than the Higgs and we expect spectacular collider signals arising from the UV framework. This includes the decay of the Higgs boson to ττℓℓ′, where ℓ(ℓ′) can be any lepton, with displaced vertices. We discuss the observational signatures of this UV framework in dark matter searches and primordial gravitational wave experiments; the latter signature is potentially correlated with the H→ττℓℓ′ decay.