Incompatibilists believe free will is impossible if determinism is true, and they often claim that this view is supported by ordinary intuitions. We challenge the claim that incompatibilism is intuitive to most laypersons and discuss the significance of this challenge to the free will debate. After explaining why incompatibilists should want their view to accord with pretheoretical intuitions, we suggest that determining whether incompatibilism is in fact intuitive calls for empirical testing. We then present the results of our studies, which put significant pressure on the claim that incompatibilism is intuitive. Finally, we consider and respond to several potential objections to our approach.