We report on the sub-kilohertz optical spectroscopy on the S-1(0)-P-3(
1) intercombination transition in magnesium at 457 nm. The spectroscop
ic signal is probed by a time domain atom interferometer. The realizat
ion of this time domain atom interferometer with laser cooled and trap
ped atoms allows extremely long interaction times and leads to resolut
ions down to 491 Hz(FWHM). This corresponds to a high line Q factor of
1.3 X 10(12). Because of the high accuracy in the determination of th
e line center, applications with respect to an optical frequency stand
ard are possible.