At the core of intelligence lies 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 thoughts and behaviors1, which has been proposed to rely on internal representations of discrete units, or symbols, and processes that can recombine them into a large set of possible composite representations1–11. 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—internal, recombinable representations of discrete units of motor behavior—localized to a specific area of frontal cortex. In macaque monkeys performing a drawing-like task designed to assess recombination of learned action symbols into novel sequences, we found behavioral evidence for three critical features that indicate actions have 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, three properties indicating a symbolic representation. Activity in no other recorded area exhibited this combination of properties. These findings reveal a neural representation of action symbols localized to PMv, and therefore identify a putative neural substrate for symbolic cognitive operations.