In comparison to 1.5 and 3 T, MR spectroscopic imaging at 7 T benefits from signal-to-noise ratio (SNR) gain and increased spectral resolution and should enable mapping of a large number of metabolites at high spatial resolutions. However, to take full advantage of the ultra-high field strength, severe technical challenges, e.g. related to very short T(2) relaxation times and strict limitations on the maximum achievable B(1) field strength, have to be resolved. The latter results in a considerable decrease in bandwidth for conventional amplitude modulated radio frequency pulses (RF-pulses) and thus to an undesirably large chemical-shift displacement artefact. Frequency-modulated RF-pulses can overcome this problem; but to achieve a sufficient bandwidth, long pulse durations are required that lead to undesirably long echo-times in the presence of short T(2) relaxation times. In this work, a new magnetic resonance spectroscopic imaging (MRSI) localization scheme (free induction decay acquisition localized by outer volume suppression, FIDLOVS) is introduced that enables MRSI data acquisition with minimal SNR loss due to T(2) relaxation and thus for the first time mapping of an extended neurochemical profile in the human brain at 7 T. To overcome the contradictory problems of short T(2) relaxation times and long pulse durations, the free induction decay (FID) is directly acquired after slice-selective excitation. Localization in the second and third dimension and skull lipid suppression are based on a T(1)- and B(1)-insensitive outer volume suppression (OVS) sequence. Broadband frequency-modulated excitation and saturation pulses enable a minimization of the chemical-shift displacement artefact in the presence of strict limits on the maximum B(1) field strength. The variable power RF pulses with optimized relaxation delays (VAPOR) water suppression scheme, which is interleaved with OVS pulses, eliminates modulation side bands and strong baseline distortions. Third order shimming is based on the accelerated projection-based automatic shimming routine (FASTERMAP) algorithm. The striking SNR and spectral resolution enable unambiguous quantification and mapping of 12 metabolites including glutamate (Glu), glutamine (Gln), N-acetyl-aspartatyl-glutamate (NAAG), gamma-aminobutyric acid (GABA) and glutathione (GSH). The high SNR is also the basis for highly spatially resolved metabolite mapping.