A scroll-type positive displacement apparatus which can be used as a vacuum pump is disclosed. A pair of interfitting scrolls are housed in a first container which communicates with a vacuum chamber to be evacuated by the pump. The scrolls are rotated in synchrony about parallel, nonaligned axes by a drive motor. The scrolls define a plurality of spiral compression chambers which change in size when the scrolls are rotated, compressing a gas contained in the compression chambers. The shaft of one of the scrolls has a discharge port formed therein which communicates between the centermost compression chamber and the inside of a second container which adjoins the first container. The second container is partially filled with lubricating oil and communicates with the atmosphere. The discharge port is equipped with a check valve which permits compressed gas to enter the second container from the scrolls but prevents gas from flowing in the opposite direction. The pump may be further equipped with one or more oil supply passageways formed in the shaft of the scroll in which the discharge port is formed. Lubricating oil is introduced via the oil supply passageway from the second container into one or more of the compression chambers of the pump.