High-temperature superconductivity has been discovered in La 2− x Ba x CuO 4 [J.G. Bednorz, K.A. Müller, Z. Phys. B 64 (1986) 189. [1]], a compound that derives from the undoped La 2CuO 4 crystallizing in the perovskite T-structure. In this structure oxygen octahedra surround the copper ions. It is common knowledge that charge carriers induced by doping in such an undoped antiferromagnetic Mott-insulator lead to high-temperature superconductivity [V.J. Emery, Phys. Rev. Lett. 58 (1987) 2794; C.M. Varma, S. Schmitt-Rink, E. Abrahams, Solid State Commun. 62 (1987) 681; E. Dagotto, Rev. Mod. Phys. 66 (1994) 763. [2–4]]. The undoped material La 2CuO 4 is also the basis of the electron-doped cuprate superconductors [Y. Tokura, H. Takagi, S. Uchida, Nature (London) 337 (1989) 345. [5]] of the form La 2− x Ce x CuO 4+ y [M. Naito, M. Hepp, Jpn. J. Appl. Phys. 39 (2000) L485; A. Sawa, M. Kawasaki, H. Takagi, Y. Tokura, Phys. Rev. B 66 (2002) 014531. [6,7]] which, however, crystallize in the so-called T′-structure, i.e. without apical oxygen above or below the copper ions of the CuO 2-plane. It is well known that for La 2− x Ce x CuO 4+ y the undoped T′-structure parent compound cannot be prepared due to the structural phase transition back into the T-structure occurring around x∼0.05. Here, we report that if La is substituted by RE=Y, Lu, Sm, Eu, Gd, or Tb, which have smaller ionic radii but have the same valence as La, nominally undoped La 2− x RE x CuO 4 can be synthesized by molecular beam epitaxy in the T′-structure. The second important result is that all these new T′-compounds are superconductors with fairly high critical temperatures up to 21 K. For this new class of cuprates La 2− x RE x CuO 4, which forms the T′-parent compounds of the La-based electron doped cuprates, we have not been able to obtain the Mott-insulating ground state for small x before the structural phase transition into the T-structure takes place.