An N-doped, p-type ZnO layer has been grown by molecular beam epitaxy on an Li-diffused, bulk, semi-insulating ZnO substrate. Hall-effect and conductivity measurements on the layer give: resistivity=4×101 Ω cm; hole mobility=2 cm2/V s; and hole concentration=9×1016 cm−3. Photoluminescence measurements in this N-doped layer show a much stronger peak near 3.32 eV (probably due to neutral acceptor bound excitons), than at 3.36 eV (neutral donor bound excitons), whereas the opposite is true in undoped ZnO. Calibrated, secondary-ion mass spectroscopy measurements show an N surface concentration of about 1019 cm−3 in the N-doped sample, but only about 1017 cm−3 in the undoped sample.