The structures of two new oxide chalcogenide phases, Sr2CuO2Cu2S2 and Sr2CuO2Cu2Se2, are reported, both of which contain infinite CuO2 planes containing Cu2+ and which have Cu+ ions in the sulfide or selenide layers. Powder neutron diffraction measurements show that Sr2CuO2Cu2Se2 exhibits long-range magnetic ordering with a magnetic structure based on antiferromagnetic interactions between nearest-neighbor Cu2+ ions, leading to a root 2a x root 2a x 2c expansion of the nuclear cell. The ordered moment of 0.39(6) mu(B) on the Cu2+ ions at 1.7 K is consistent with the value predicted by density functional theory calculations. The compounds are structurally related to the cuprate superconductors and may also be considered as analogues of the parent phases of this class of superconductor such as Sr2CuO2Cl2 or La2CuO4. In the present case, however, the top of the chalcogenide-based valence band is very close to the vacant Cu2+ 3d states of the conduction band, leading to relatively high measured conductivity.