Personality neuroscience aims to find associations between brain measures and personality traits. Findings to date have been severely limited by a number of factors, including small sample size and omission of out-of-sample prediction. We capitalized on the recent availability of a large database, together with the emergence of specific criteria for best practices in neuroimaging studies of individual differences. We analyzed resting-state functional magnetic resonance imaging (fMRI) data from 884 young healthy adults in the Human Connectome Project database. We attempted to predict personality traits from the “Big Five,” as assessed with the Neuroticism/Extraversion/Openness Five-Factor Inventory test, using individual functional connectivity matrices. After regressing out potential confounds (such as age, sex, handedness, and fluid intelligence), we used a cross-validated framework, together with test-retest replication (across two sessions of resting-state fMRI for each subject), to quantify how well the neuroimaging data could predict each of the five personality factors. We tested three different (published) denoising strategies for the fMRI data, two intersubject alignment and brain parcellation schemes, and three different linear models for prediction. As measurement noise is known to moderate statistical relationships, we performed final prediction analyses using average connectivity across both imaging sessions (1 hr of data), with the analysis pipeline that yielded the highest predictability overall. Across all results (test/retest; three denoising strategies; two alignment schemes; three models), Openness to experience emerged as the only reliably predicted personality factor. Using the full hour of resting-state data and the best pipeline, we could predict Openness to experience (NEOFAC_O: r=.24, R2=.024) almost as well as we could predict the score on a 24-item intelligence test (PMAT24_A_CR: r=.26, R2=.044). Other factors (Extraversion, Neuroticism, Agreeableness, and Conscientiousness) yielded weaker predictions across results that were not statistically significant under permutation testing. We also derived two superordinate personality factors (“α” and “β”) from a principal components analysis of the Neuroticism/Extraversion/Openness Five-Factor Inventory factor scores, thereby reducing noise and enhancing the precision of these measures of personality. We could account for 5% of the variance in the β superordinate factor (r=.27, R2=.050), which loads highly on Openness to experience. We conclude with a discussion of the potential for predicting personality from neuroimaging data and make specific recommendations for the field.