The neutron-rich unbound 7He nucleus has been the subject of many experimental investigations. While the ground-state 3/2- resonance is well established, there is a controversy concerning the excited 1/2- resonance reported in some experiments as low lying and narrow (E(R)∼1 MeV, Γ≤1 MeV) while in others as very broad and located at a higher energy. This issue cannot be addressed by ab initio theoretical calculations based on traditional bound-state methods. We introduce a new unified approach to nuclear bound and continuum states based on the coupling of the no-core shell model, a bound-state technique, with the no-core shell model combined with the resonating-group method, a nuclear scattering technique. Our calculations describe the ground-state resonance in agreement with experiment and, at the same time, predict a broad 1/2- resonance above 2 MeV.