It has been proposed that interactions between mammalian chromosomes, or transchromosomal interactions (also known as kissing chromosomes), regulate gene expression and cell fate determination. Here we aimed to identify novel transchromosomal interactions in immune cells by high-resolution genome-wide chromosome conformation capture. Although we readily identified stable interactions in cis, and also between centromeres and telomeres on different chromosomes, surprisingly we identified no gene regulatory transchromosomal interactions in either mouse or human cells, including previously described interactions. We suggest that advances in the chromosome conformation capture technique and the unbiased nature of this approach allow more reliable capture of interactions between chromosomes than previous methods. Overall our findings suggest that stable transchromosomal interactions that regulate gene expression are not present in mammalian immune cells and that lineage identity is governed by cis, not trans chromosomal interactions.