Causal networks are widely used in many fields to model the complex relationships between variables. A recent approach has sought to construct causal networks by leveraging the wisdom of crowds through the collective participation of humans. While this can yield detailed causal networks that model the underlying phenomena quite well, it requires a large number of individuals with domain understanding. We adopt a different approach: leveraging the causal knowledge that large language models, such as OpenAI's GPT-4, have learned by ingesting massive amounts of literature. Within a dedicated visual analytics interface, called CausalChat, users explore single variables or variable pairs recursively to identify causal relations, latent variables, confounders, and mediators, constructing detailed causal networks through conversation. Each probing interaction is translated into a tailored GPT-4 prompt and the response is conveyed through visual representations which are linked to the generated text for explanations. We demonstrate the functionality of CausalChat across diverse data contexts and conduct user studies involving both domain experts and laypersons.