Chromatin acts as a key regulator of DNA‐related processes such as DNA damage repair. Although ChIP‐chip is a powerful technique to provide high‐resolution maps of protein–genome interactions, its use to study DNA double strand break (DSB) repair has been hindered by the limitations of the available damage induction methods. We have developed a human cell line that permits induction of multiple DSBs randomly distributed and unambiguously positioned within the genome. Using this system, we have generated the first genome‐wide mapping of γH2AX around DSBs. We found that all DSBs trigger large γH2AX domains, which spread out from the DSB in a bidirectional, discontinuous and not necessarily symmetrical manner. The distribution of γH2AX within domains is influenced by gene transcription, as parallel mappings of RNA Polymerase II and strand‐specific expression showed that γH2AX does not propagate on active genes. In addition, we showed that transcription is accurately maintained within γH2AX domains, indicating that mechanisms may exist to protect gene transcription from γH2AX spreading and from the chromatin rearrangements induced by DSBs.