Heavy few-electron ions, such as He-, Li- and Be-like ions, are ideal atomic systems to study the effects of correlation, relativity and quantum electrodynamics. Very recently, theoretical and experimental studies of these species achieved a considerable improvement in accuracy. Be-like ions are interesting because their first excited state, i.e. (1s(2)2s2p) P-3(0), has an almost infinite lifetime (tau(0)) in the absence of nuclear spin (I), as it can only decay by a two-photon E1M1 transition to the (1s(2)2s(2)) S-1(0) ground state. In addition, the energy difference between the 3P0 and the next higher-lying P-3(1) state is expected to remain almost completely unaffected by QED effects, and should thus be dominated by the effects of correlation and relativity. Therefore, we want to determine the (1s(2)2s2p) P-3(0)-P-3(1) level splitting in Be-like krypton (Kr-84(32+)), which has I = 0, by means of laser spectroscopy at the experimental storage ring at GSI. In such an experiment, the energy splitting can be obtained with very good accuracy and can be compared with recent calculations.