Can personality be predicted from oscillatory patterns produced by the brain at rest? To date, relatively few studies using electroencephalography (EEG) have yielded consistent relations between personality trait measures and spectral power. Thus, new exploratory research may help develop targeted hypotheses about how neural processes associated with EEG activity may relate to personality differences. We used multivariate pattern analysis to decode personality scores (i.e., Big Five traits) from resting EEG frequency power spectra. Up to 8 minutes of EEG data was recorded per participant prior to completing an unrelated task (N = 168, Mage = 23.51, 57% female) and, in a subset of participants, after task completion (N = 96, Mage = 23.22, 52% female). In each recording, participants alternated between open and closed eyes. Linear support vector regression with 10-fold cross validation was performed using the power from 62 scalp electrodes within 1 Hz frequency bins from 1 to 30 Hz. One Big Five trait, agreeableness, could be decoded from EEG power ranging from 8 to 19 Hz, and this was consistent across all four recording periods. Neuroticism was decodable using data within the 3–6 Hz range, albeit less consistently. Posterior alpha power negatively correlated with agreeableness, whereas parietal beta power positively correlated with agreeableness. We suggest methods to draw from our results and develop targeted future hypotheses, such as linking to individual alpha frequency and incorporating self-reported emotional states. Our open dataset can be harnessed to reproduce results or investigate new research questions concerning the biological basis of personality.