The design and performance of an apparatus for measuring magnetic susceptibility using a superconducting magnetometer and superconducting magnet and shields are described. Measurements of static susceptibility and of nuclear magnetic resonance have been made with this system. Volume susceptibility changes of 10−10cgs can be measured with a 1 sec response time, a 100 Oe applied field, and a 1 cm3sample. Noise limitations and potential for improvement of sensitivity by several orders of magnitude are discussed.