In a conversational question answering scenario, a questioner seeks to extract information about a topic through a series of interdependent questions and answers. As the conversation progresses, they may switch to related topics, a phenomenon commonly observed in information-seeking search sessions. However, current datasets for conversational question answering are limiting in two ways: 1) they do not contain topic switches; and 2) they assume the reference text for the conversation is given, that is, the setting is not open-domain. We introduce TopiOCQA (pronounced Tapioca), an open-domain conversational dataset with topic switches based on Wikipedia. TopiOCQA contains 3,920 conversations with information-seeking questions and free-form answers. On average, a conversation in our dataset spans 13 question-answer turns and involves four topics (documents). TopiOCQA poses a challenging test-bed for models, where efficient retrieval is required on multiple turns of the same conversation, in conjunction with constructing valid responses using conversational history. We evaluate several baselines, by combining state-of-the-art document retrieval methods with neural reader models. Our best model achieves F1 of 55.8, falling short of human performance by 14.2 points, indicating the difficulty of our dataset. Our dataset and code are available at https://mcgill-nlp.github.io/topiocqa .