The magnetic field dependence of the chemical potential of an electron system can be measured using a metallic single-electron transistor (SET). To demonstrate the method, a SET made of aluminum was fabricated on top of a GaAs/AlGaAs heterostructure containing a two-dimensional electron system (2DES). A change in the chemical potential of the 2DES causes a change in the contact voltage between the SET leads and the 2DES below the SET island which affects the current flow through the SET island. Tuning a voltage which is externally applied in series to the contact voltage, the change in the intrinsic contact voltage can be compensated to keep the SET current constant. With this tuning voltage, the change of the chemical potential by the magnetic field is directly measured. The method described here is applicable to other materials and other parameters affecting the intrinsic contact voltages. ©1997 American Institute of Physics.