The weakly bound exotic Be11 nucleus, famous for its ground-state parity inversion and distinct n+Be10 halo structure, is investigated from first principles using chiral two- and three-nucleon forces. An explicit treatment of continuum effects is found to be indispensable. We study the sensitivity of the Be11 spectrum to the details of the three-nucleon force and demonstrate that only certain chiral interactions are capable of reproducing the parity inversion. With such interactions, the extremely large E1 transition between the bound states is reproduced. We compare our photodisintegration calculations to conflicting experimental data and predict a distinct dip around the 3/21- resonance energy. Finally, we predict low-lying 3/2+ and 9/2+ resonances that are not or not sufficiently measured in experiments.