The structure of the extremely proton-rich nucleus _{8}^{11}O_{3}, the mirror of the two-neutron halo nucleus _{3}^{11}Li_{8}, has been studied experimentally for the first time. Following two-neutron knockout reactions with a ^{13}O beam, the ^{11}O decay products were detected after two-proton emission and used to construct an invariant-mass spectrum. A broad peak of width ∼3.4 MeV was observed. Within the Gamow coupled-channel approach, it was concluded that this peak is a multiplet with contributions from the four lowest ^{11}O resonant states: J^{π}=3/2_{1}^{-}, 3/2_{2}^{-}, 5/2_{1}^{+}, and 5/2_{2}^{+}. The widths and configurations of these states show strong, nonmonotonic dependencies on the depth of the p-^{9}C potential. This unusual behavior is due to the presence of a broad threshold resonant state in ^{10}N, which is an analog of the virtual state in ^{10}Li in the presence of the Coulomb potential. After optimizing the model to the data, only a moderate isospin asymmetry between ground states of ^{11}O and ^{11}Li was found.