We study the optimal placement of advertisements for interactive platforms like conversational AI assistants. Importantly, conversations add a feature absent in canonical search markets -- time. The evolution of a conversation is informative about ad qualities, thus a platform could delay ad delivery to improve selection. However, delay endogenously shapes the supply of quality ads, possibly affecting revenue. We characterize the equilibria of first- and second-price auctions where the platform can commit to the auction format but not to its timing. We document sharp differences in the mechanisms' outcomes: first-price auctions are efficient but delay ad delivery, while second-price auctions avoid delay but allocate inefficiently. Revenue may be arbitrarily larger in a second-price auction than in a first-price auction. Optimal reserve prices alleviate these differences but flip the revenue ordering.