People’s ability to think creatively is a primary means of technological and cultural progress, yet the neural architecture of the highly creative brain remains largely undefined. Here, we employed a recently developed method in functional brain imaging analysis—connectome-based predictive modeling—to identify a brain network associated with high-creative ability, using functional magnetic resonance imaging (fMRI) data acquired from 163 participants engaged in a classic divergent thinking task. At the behavioral level, we found a strong correlation between creative thinking ability and self-reported creative behavior and accomplishment in the arts and sciences (r = 0.54). At the neural level, we found a pattern of functional brain connectivity related to high-creative thinking ability consisting of frontal and parietal regions within default, salience, and executive brain systems. In a leave-one-out cross-validation analysis, we show that this neural model can reliably predict the creative quality of ideas generated by novel participants within the sample. Furthermore, in a series of external validation analyses using data from two independent task fMRI samples and a large task-free resting-state fMRI sample, we demonstrate robust prediction of individual creative thinking ability from the same pattern of brain connectivity. The findings thus reveal a whole-brain network associated with high-creative ability comprised of cortical hubs within default, salience, and executive systems—intrinsic functional networks that tend to work in opposition—suggesting that highly creative people are characterized by the ability to simultaneously engage these large-scale brain networks.