We report on the first direct measurement of the g-factor of a highly charged ion. The experimental determination of the magnetic moment (g-factor) of the bound electron in hydrogen-like ions is an important test of the theory of Quantum Electrodynamics in strong nuclear Coulomb fields. For this purpose a single hydrogen-like ion is stored in the magnetic field of a Penning trap. The g-factor is measured by inducing spin flip transitions with a microwave field at the Larmor precession frequency of the bound electron. The magnetic field is calibrated by measuring the cyclotron frequency of the stored ion. The first results were obtained for a hydrogen-like carbon ion(C5+).The experimental precision is high enough to verify the relativistic contribution to the g-factor on the10−3level. ©1999 American Institute of Physics.