The electrical activity in the very early human preterm brain, as recorded by scalp EEG, is mostly discontinuous and has bursts of high-frequency oscillatory activity nested within slow-wave depolarisations of high amplitude. The temporal organisation of the occurrence of these EEG bursts has not been previously investigated. We analysed the distribution of the EEG bursts in 11 very preterm (23-30 weeks gestational age) human babies through two estimates of the Hurst exponent. We found long-range temporal correlations (LRTCs) in the occurrence of these EEG bursts demonstrating that even in the very immature human brain, when the cerebral cortical structure is far from fully developed, there is non-trivial temporal structuring of electrical activity.