Intracranial electroencephalography (iEEG) data offer a unique combination of high spatial and temporal resolution measures of the living human brain. However, data collection is limited to highly specialized clinical environments. To improve internal (re)use and external sharing of these unique data, we present a structure for storing and sharing iEEG data: BIDS-iEEG, an extension of the Brain Imaging Data Structure (BIDS) specification, along with freely available examples and a bids-starter-kit. BIDS is a framework for organizing and documenting data and metadata with the aim to make datasets more transparent and reusable and to improve reproducibility of research. It is a community-driven specification with an inclusive decision-making process. As an extension of the BIDS specification, BIDS-iEEG facilitates integration with other modalities such as fMRI, MEG, and EEG. As the BIDS-iEEG extension has received input from many iEEG researchers, it provides a common ground for data transfer within labs, between labs, and in open-data repositories. It will facilitate reproducible analyses across datasets, experiments, and recording sites, allowing scientists to answer more complex questions about the human brain. Finally, the cross-modal nature of BIDS will enable efficient consolidation of data from multiple sites for addressing questions about generalized brain function.