From cockroaches to human beings, the presence of other members of the same species typically facilitates dominant (habitual/well-learned) responses regardless of their contextual relevance. This social facilitation requires special attention in animal species such as primates, given their evolved cognitive control mechanisms. Here we tested baboons who freely engaged in (computer-based) conflict response tasks requiring cognitive control for successful performance, and discovered that social presence does not only enhance dominant responses but also consumes cognitive control resources. Under social presence, the baboons experienced greater cognitive conflicts, were less able to inhibit a learned action in favor of a new one, and were also less able to take advantage of previous experience with response conflict, compared with isolation. These findings explain why inappropriate behaviors are not easily suppressed in primates acting in social contexts, and indicate a greater demand for cognitive control in social groups. This extra demand might represent a major evolutionary drive of human intelligence.