By now a consensus has emerged that people, when subjected to high-stakes decisions through automated decision systems, have a moral right to have these decisions explained to them. However, furnishing such explanations can be costly. So the right to an explanation creates what we call the cost problem: providing subjects of automated decisions with appropriate explanations of the grounds of these decisions can be costly for the companies and organisations that use these automated decision systems. In this paper, we explore (...) whether large language models could prove significant in overcoming the cost problem. We provide an initial case for believing that they can but only with serious ethical costs. (shrink)