We have observed β−β−-delayed proton emission from the neutron-rich nucleus 11Be by analyzing a sample collected at the ISOLDE facility at CERN with accelerator mass spectrometry (AMS). With a branching ratio of (8.3±0.9)⋅10−6(8.3±0.9)⋅10−6 the strength of this decay mode, as measured by the BGTBGT-value, is unexpectedly high. The result is discussed within a simple single-particle model and could be interpreted as a quasi-free decay of the 11Be halo neutron into a single-proton state.