Humans are often inconsistent (irrational) when choosing among simple bundles of goods, even without any particular changes to framing or context. However, the neural computations that give rise to such inconsistencies are still unknown. Similar to sensory perception and motor output, we propose that a substantial component of inconsistent behavior is due to variability in the neural computation of value. Here, we develop a novel index that measures the severity of inconsistency of each choice, enabling us to directly trace its neural correlates. We find that the BOLD signal in the vmPFC, ACC, and PCC is correlated with the severity of inconsistency on each trial and with the subjective value of the chosen alternative. This suggests that deviations from rational choice arise in the regions responsible for value computation. We offer a computational model of how variability in value computation is a source of inconsistent choices.