Knowledge-grounded dialogue agents are systems designed to conduct a conversation based on externally provided background information, such as a Wikipedia page. Such dialogue agents, especially those based on neural network language models, often produce responses that sound fluent but are not justified by the background information. Progress towards addressing this problem requires developing automatic evaluation metrics that can quantify the extent to which responses are grounded in background information. To facilitate evaluation of such metrics, we introduce the Benchmark for Evaluation of Grounded INteraction (BEGIN). BEGIN consists of 8113 dialogue turns generated by language-model-based dialogue systems, accompanied by humans annotations specifying the relationship between the system's response and the background information. These annotations are based on an extension of the natural language inference paradigm. We use the benchmark to demonstrate the effectiveness of adversarially generated data for improving an evaluation metric based on existing natural language inference datasets.