A lock box includes a pair of box-like base and cover structures having side and end walls configured to overlap when the base structure is nestingly received in the cover structure. A key-operated lock is carried on the cover structure and is engageable with a receiving formation provided on the base structure. Interfitting formations are provided on the base and cover structures to assist the key-operated lock in releasably retaining the cover structure in place on the base structure. The base structure has a back wall which may be fastened to a mounting surface.