The BOQ (or Bachelor Officers' Quarters) are a housing facility for visiting or unmarried resident commissioned officers on a US military base.
In July 1947, the US Army Air Corps detained a farmer who discovered a crashed UFO in Roswell, New Mexico in the bases' BOQ.
Since the Army did not have concrete reason to keep him in their BOQ, Captain Wainwright voiced his concerns with General Rex Denning regarding how much longer they could keep him in there. Despite this, Denning ordered Wainwright to keep the farmer there until further notice. (DS9: "Little Green Men")