Lattice QCD calculations at finite temperature and zero or small baryon chemical potential have shown that there is no phase transition separating quasi-free quarks and those confined in baryons. Quarkyonic matter is a hypothetical state where quarks and baryons can coexist in a single Fermi sphere; quarks occupy the low momenta levels, hadrons the high momenta ones. This paper puts forward the idea that normal nuclear matter may, in fact, be quarkyonic and that the existence of this exotic phase may already have been seen in current electron-nucleus scattering data.