  We present the first terrestrial measurement of the Lande g factor of the
5D5/2 state of singly ionized barium. Measurements were performed on single
Doppler-cooled 138Ba+ ions in a linear Paul trap. A frequency-stabilized fiber
laser with nominal wavelength 1.762 um was scanned across the 6S1/2<->5D5/2
transition to spectroscopically resolve transitions between Zeeman sublevels of
the ground and excited states. From the relative positions of the four narrow
transitions observed at several different values for the applied magnetic
field, we find a value of 1.2020+/-0.0005 for g of 5D5/2.
