What makes a proposition true or false has traditionally played an essential role in philosophical and linguistic theories of meaning. A comprehensive neurobiological theory of language must ultimately be able to explain the combined contributions of real-world truth-value and discourse context to sentence meaning. This fMRI study investigated the neural circuits that are sensitive to the propositional truth-value of sentences about counterfactual worlds, aiming to reveal differential hemispheric sensitivity of the inferior prefrontal gyri to counterfactual truth-value and real-world truth-value. Participants read true or false counterfactual conditional sentences (“If N.A.S.A. had not developed its Apollo Project, the first country to land on the moon would be Russia/America”) and real-world sentences (“Because N.A.S.A. developed its Apollo Project, the first country to land on the moon has been America/Russia”) that were matched on contextual constraint and truth-value. ROI analyses showed that whereas the left BA 47 showed similar activity increases to counterfactual false sentences and to real-world false sentences (compared to true sentences), the right BA 47 showed a larger increase for counterfactual false sentences. Moreover, whole-brain analyses revealed a distributed neural circuit for dealing with propositional truth-value. These results constitute the first evidence for hemispheric differences in processing counterfactual truth-value and real-world truth-value, and point toward additional right hemisphere involvement in counterfactual comprehension.