Investment in basic science is mainly supported by government funding, but little is known about citizens' willingness to pay for large-scale projects. A survey to a representative sample of French taxpayers, designed as a contingent valuation experiment about a future particle accelerator for CERN, reveals that citizens' willingness to pay is correlated with education, income, age, and-crucially-previous awareness, attitudes and interest in science. A (slim) majority of the participants would accept paying more in taxes for CERN. The estimated willingness to pay is higher than the current implicit per capita tax burden of French citizens. The experimental setting is novel and replicable for empirically assessing social attitudes towards science for other research infrastructures and countries.