Anecdotal reports suggest the existence of individual differences in peoples' cognitive styles for solving problems, in particular, the tendency to rely on insight (the "aha" phenomenon) versus deliberate analytical thought. We hypothesized that such stable individual differences exist and are associated with trait-like individual differences in resting-state brain activity. We tested this idea by recording participants' resting-state electroencephalograms (RS-EEGs) on 4 occasions over approximately 7 weeks and then tasking them with solving anagrams and compound remote associates problems that are solvable by either strategy. We found that peoples' tendency to solve problems consistently by insight or by analysis spans both tasks and time. Moreover, we discovered trait-like individual differences in the balance between frontal and posterior resting-state brain activity and in temporal-lobe hemispheric asymmetries that predict, at least weeks in advance, the tendency to solve by insight versus analysis. The discovery of an insight-analytic dimension of cognitive style and its neural basis in resting state brain activity suggests new avenues for the development of neuroscience-based methods for intellectual, educational, and vocational assessment.