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Self-similarities at different time scales embedded within a self-organizing neural manifold are well recognized. In this study, we hypothesize that the Hurst fractal dimension (HFD) of the scalp electroencephalographic (EEG) signal reveals statistical differences between chronic pain and opioid use. We test this hypothesis by using EEG resting state signals acquired from a total of 23 human subjects: 14 with chronic pain, 9 with chronic pain taking opioid medications, 5 with chronic pain and not taking opioid medications, and 9 healthy controls. Using the multifractal analysis algorithm, the HFD for full spectrum EEG and EEG frequency band time series was computed for all groups. Our results indicate the HFD varies spatially and temporally across all groups and is of lower magnitude in patients not taking opioids as compared to those taking opioids and healthy controls. A global decrease in HFD was observed with changes in gamma and beta power in the chronic pain group compared to controls and when paired to subject handedness and sex. Our results show the loss of complexity representative of brain wide dysfunction and reduced neural processing can be used as an EEG biomarker for chronic pain and subsequent opioid use.