Access to well-defined ubiquitin conjugates has been key to elucidating the biochemical functions of proteins in the ubiquitin signaling network. Yet, we have a poor understanding of how deubiquitinases and ubiquitin-binding proteins respond to ubiquitin modifications when anchored to a protein other than ubiquitin or a ubiquitin-like protein. This is due to the difficulty of synthesizing ubiquitinated proteins comprised of native isopeptide bonds. Here we report on the evolution of a deubiquitinase capable of site-specifically modifying itself with defined ubiquitin chains. Following mutagenesis and yeast display screening, we identify a variant of the yeast ubiquitin C-terminal hydrolase Yuh1 that has a 28-fold improvement in the transamidation to hydrolysis ratio relative to the wild type enzyme. The switch in activity enables robust autoubiquitination of a lysine in the crossover loop to form an isopeptide bond. We demonstrate the utility of autoubiquitinating the evolved Yuh1 variant by investigating the consequences of ubiquitin chain anchoring on the activities of other deubiquitinases. Much to our surprise, we find that certain deubiquitinases are exquisitely sensitive to chain anchoring. These results highlight the importance of investigating the biochemical activities of deubiquitinases with both substrate-anchored and unanchored ubiquitin chains.