Room-temperature precipitation from aqueous solutions yields the hitherto unknown metastable stoichiometric iron selenide (ms-FeSe) with tetragonal anti-PbO type structure. Samples with improved crystallinity are obtained by diffusion-controlled precipitation or hydrothermal recrystallization. The relations of ms-FeSe to superconducting beta-FeSe1-x and other neighbor phases of the iron selenium system are established by high-temperature X-ray diffraction, DSC/TG/MS (differential scanning calorimetry/thermogravimetry/mass spectroscopy), Fe-57 Mossbauer spectroscopy, magnetization measurements, and transmission electron microscopy. Above 300 degrees C, ms-FeSe decomposes irreversibly to beta-FeSe1-x and Fe7Se8. The structural parameters of ms-FeSe (P4/nmm, a = 377.90(1) pm, c = 551.11(3) pm, Z = 2), obtained by Rietveld refinement, differ significantly from literature data for beta-FeSe1-x. The Mossbauer spectrum rules out interstitial iron atoms or additional phases. Magnetization data suggest canted antiferromagnetism below T-N = 50 K. Stoichiometric non-superconducting ms-FeSe can be regarded as the true "parent" compound for the "11" iron-chalcogenide superconductors and may serve as starting point for new chemical modifications.