Work in information retrieval has traditionally been focused on ranking and relevance: for a user's query, fetch some number of results, ordered by relevance to the user. However, the problem of determining how many results to return, i.e. how to optimally truncate the ranked result list, has received far less attention despite being of critical importance in a range of applications. Such truncation is a balancing act between the overall relevance, or usefulness, of the results with the user cost of processing more results. In this work, we propose Choppy, an assumption-free model based on the widely successful Transformer architecture in NLP, to the ranked-list truncation problem. Needing nothing more than the relevance scores of the results, the model uses a powerful multi-head attention mechanism to directly optimize any user-defined target IR metric. We show Choppy improves upon recent, state-of-the-art baselines on Robust04.