Each year, over a hundred thousand defendants who are too poor to pay for a lawyer are assigned counsel. Existing procedures for making such assignments are essentially random and have been criticized for giving indigent defendants no say in choosing the counsel they are assigned to. In this paper, we model the problem of assigning counsel to indigent defendants as a matching problem. A novel aspect of this matching problem is the moral hazard component on the part of counsel. Within the model, we show that holding the total expenditure for counsel fixed and changing the matching procedure to accommodate defendants' and attorneys' preferences will make defendants worse off. More precisely, if we switch from random matching to stable matching, defendants become worse off because stable matching exacerbates the moral hazard problem on the part of counsel. In addition, we find conditions on reservation wages of attorneys under which random matching is the efficient way to allocate defendants to counsel.