We propose a simple theory for the idea that cosmological dark matter (DM) may be present today mainly in the form of stable neutral hadronic thermal relics. In our model, neutrino masses arise radiatively from the exchange of colored DM constituents, giving a common origin for both dark matter and neutrino mass. The exact conservation of $B\ensuremath{-}L$ symmetry ensures dark matter stability and the Dirac nature of neutrinos. The theory can be falsified by dark matter nuclear recoil direct detection experiments, leading also to possible signals at a next generation hadron collider.