A hallmark of intelligence is proficiency in solving new problems, including those that differ dramatically from problems seen before. Problem-solving, in turn, depends on goal-directed generation of novel ideas and behaviors 1 , which has been proposed to rely on internal representations of discrete units, or symbols, and processes that recombine these units into a large set of possible composite representations 1–9 . Although this view has been influential in formulating cognitive-level explanations of behavior, definitive evidence for a neuronal substrate of symbols has remained elusive. Here, we identify a neural population encoding action symbols—recombinable representations of discrete units of motor behavior—localized to a specific area of frontal cortex. In macaque monkeys performing a drawing-like task, we found behavioral evidence that action elements (strokes) exhibit three critical features indicating an underlying symbolic representation: (i) invariance over low-level motor parameters; (ii) categorical structure, reflecting discrete types of action; and (iii) recombination into novel sequences. In simultaneous neural recordings across motor, premotor, and prefrontal cortex, we found that planning-related population activity in ventral premotor cortex (PMv) encodes actions in a manner that, like behavior, reflects motor invariance, categorical structure, and recombination. Activity in no other recorded area exhibited these three properties of symbols. These findings reveal a neural representation of action symbols localized to PMv, and therefore identify a putative neural substrate for symbolic cognitive operations.