We present an atom interferometer based on the interference of three p
artial matter waves in three different internal and external states. C
oherent laser excitation acts as a beamsplitter to create a superposit
ion state of the ground state and two Zeeman sublevels of the metastab
le state of magnesium atoms. The interference pattern of the output po
rts shows high contrast and the characteristics of three-beam interfer
ences as known from optical interferometry. In comparison to two-beam
interferometry a reduction of the fringe width of (32+/-8)% is observe
d. This offers various possibilities for improved measurements of quan
tum-mechanical phases due to the internal atomic-state sensitive coupl
ing of external potentials. This is demonstrated for the interaction o
f magnesium atoms with an external magnetic field.