When do conversations lead people to generate better ideas? We conducted a field experiment at a startup boot camp to evaluate the impact of informal conversations on the quality of product ideas generated by participants. Specifically, we examine how the personality of an innovator (openness to experience, capturing creativity) and the personalities of her randomly assigned conversational peers (extroversion, measuring willingness to share information) affects the innovator's ideas. We find that open innovators who spoke with extroverted peers generated significantly better ideas than others at the boot camp. However, closed individuals produced mediocre ideas regardless of the individuals they interviewed, suggesting limited benefits of conversations for these people. More surprisingly, open individuals, who are believed to be inherently creative, produced worse ideas after they spoke with introverted peers, suggesting individual creativity's dependence on external information. Our study demonstrates the importance of considering the traits of both innovators and their conversational peers in predicting who will generate the best ideas.