Chromatin interaction data from protocols such as ChIA-PET, HiChIP and Hi-C provide valuable insights into genome organization and gene regulation, but can include spurious interactions that do not reflect underlying genome biology. We introduce an extension of the Irreproducible Discovery Rate (IDR) method called IDR2D that identifies replicable interactions shared by chromatin interaction experiments. IDR2D provides a principled set of interactions and eliminates artifacts from single experiments. The method is available as a Bioconductor package for the R community, as well as an online service at https://idr2d.mit.edu.National Institutes of Health (Grants 1R01HG008363 and 1R01NS078097)