To build open-domain chatbots that are able to use diverse communicative skills, we propose a novel framework BotsTalk, where multiple agents grounded to the specific target skills participate in a conversation to automatically annotate multi-skill dialogues. We further present Blended Skill BotsTalk (BSBT), a large-scale multi-skill dialogue dataset comprising 300K conversations. Through extensive experiments, we demonstrate that our dataset can be effective for multi-skill dialogue systems which require an understanding of skill blending as well as skill grounding. Our code and data are available at https://github.com/convei-lab/BotsTalk.