We introduce the new task of domain name dispute resolution (DNDR), that predicts the outcome of a process for resolving disputes about legal entitlement to a domain name. TheICANN UDRP establishes a mandatory arbitration process for a dispute between a trade-mark owner and a domain name registrant pertaining to a generic Top-Level Domain (gTLD) name (one ending in .COM, .ORG, .NET, etc). The nature of the problem leads to a very skewed data set, which stems from being able to register a domain name with extreme ease, very little expense, and no need to prove an entitlement to it. In this paper, we describe thetask and associated data set. We also present benchmarking results based on a range of mod-els, which show that simple baselines are in general difficult to beat due to the skewed data distribution, but in the specific case of the respondent having submitted a response, a fine-tuned BERT model offers considerable improvements over a majority-class model