Hyperspectral Imaging (HSI) is a relatively new medical imaging modality that exploits an area of diagnostic potential formerly untouched. Although exploratory translational and clinical studies exist, no surgical HSI datasets are openly accessible to the general scientific community. To address this bottleneck, this publication releases HeiPorSPECTRAL (https://www.heiporspectral.org), the first annotated high-quality standardized HSI dataset. It comprises 5,758 spectral images acquired with the TIVITA Tissue and annotated with 20 physiological porcine organs in a total number of 11 pigs. Each HSI image features a resolution of 480 x 640 pixels acquired over the 500-1000 nm wavelength range. The acquisition protocol has been designed such that the variability of organ spectra as a function of several parameters including the camera pose and the individual can be assessed. A comprehensive technical validation confirmed both the quality of the raw data and the annotations. We envision potential reuse within this dataset, but also its reuse as baseline data for future research questions outside this dataset, such as the detection of pathologies.