Conversation is generally characterized by smooth transitions between turns, with only very short gaps. This entails that responders often begin planning their response before the ongoing turn is finished. However, controversy exists about whether they start planning as early as they can, to make sure they respond on time, or as late as possible, to minimize the overlap between comprehension and production planning. Two earlier EEG studies have found neural correlates of response planning (positive ERP and alpha decrease) as soon as listeners could start planning their response, already midway through the current turn. However, in these studies, the questions asked were highly controlled with respect to the position where planning could start (e.g., very early) and required short and easy responses. The present study measured participants' EEG while an experimenter interviewed them in a spontaneous interaction. Coding the questions in the interviews showed that, under these natural circumstances, listeners can, in principle, start planning a response relatively early, on average after only about one third of the question has passed. Furthermore, ERP results showed a large positivity, interpreted before as an early neural signature of response planning, starting about half a second after the start of the word that allowed listeners to start planning a response. A second neural signature of response planning, an alpha decrease, was not replicated as reliably. In conclusion, listeners appear to start planning their response early during the ongoing turn, also under natural circumstances, presumably in order to keep the gap between turns short and respond on time. These results have several important implications for turn-taking theories, which need to explain how interlocutors deal with the overlap between comprehension and production, how they manage to come in on time, and the sources that lead to variability between conversationalists in the start of planning.