Languages tend to encode events from the perspective of agents, placing them first and in simpler forms than patients. This agent bias is mirrored by cognition: Agents are more quickly recognized than patients and generally attract more attention. This leads to the hypothesis that key aspects of language structure are fundamentally rooted in a cognition that decomposes events into agents, actions, and patients, privileging agents. Although this type of event representation is almost certainly universal across languages, it remains unclear whether the underlying cognition is uniquely human or more widespread in animals. Here, we review a range of evidence from primates and other animals, which suggests that agent-based event decomposition is phylogenetically older than humans. We propose a research program to test this hypothesis in great apes and human infants, with the goal to resolve one of the major questions in the evolution of language, the origins of syntax.