Operation of and XUV free electron laser (FEL) oscillator in the 27 m straight section of the 1 GeV Stanford X-Ray Center (SXRC) storage ring is examined. Based on high gain calculations made with the help of the FEL amplifier simulation code FRED, oscillation below 1000 Å is found to be readily achievable. FEL longitudinal and transverse acceptances in the high gain regime for a constant parameter wiggler are investigated. Estimates are made of peak and average output powers for 960 Å and 285 Å oscillators operating in the storage ring cw mode. The case of a 960 Å oscillator operating in the pulsed mode is also investigated. Time structures for both modes are calculated for single and multi-bunch ring operation.