Using the Becke-3-LYP functional, we have performed band structure calculations on the high temperature superconductor parent compound, La2CuO4. For the restricted spin paramagnetic case (rho(alpha) equal to rho(beta)), the B3LYP band structure agrees well with the standard LDA band structure. It has a metallic ground state with a single Cu x2-y2/O p(sigma) band crossing the Fermi level. For the unrestricted spin case (rho(alpha) not equal to rho(beta)), a spin polarized antiferromagnetic state is found with a band gap of 2.0 eV, agreeing well with experiment. This state is 1.0 eV (per formula unit) lower than the calculated paramagnetic state. This large energy difference is particularly startling given that the ferromagnetic state is also calculated to be 0.82 eV lower than the paramagnetic state. The apparent high energy of the spin restricted state is attributed to an overestimate of on-site Coulomb repulsion which is corrected in the unrestricted spin calculations. The stabilization of the total energy with spin polarization arises primarily from the stabilization of the x2-y2 band, such that the character of the eigenstates at the top of the valence band in the antiferromagnetic state becomes a strong mixture of Cu x2-y2/O p(sigma) and Cu z2/O' p(z). Since the Hohenberg-Kohn theorem requires the spin restricted and spin unrestricted calculations give exactly the same ground state energy and total density, this large disparity in energy reflects the inadequacy of current functionals for describing the cuprates. It seriously calls into question the use of any present-day restricted spin density functional band structure (including LDA) as a basis for single band theories of superconductivity in these materials.