Protein domains that act as degradation and stabilization signals regulate the rate of turnover of proteasomal substrates. Here we report that the bipartite Gly-Arg repeat of the Epstein-Barr virus (EBV) nuclear antigen (EBNA)-1 acts as a stabilization signal that inhibits proteasomal degradation in the nucleus by promoting binding to cellular DNA. Protection can be transferred by grafting the domain to unrelated proteasomal substrates and does not involve changes of ubiquitylation. Protection is also afforded by other protein domains that, similar to the Gly-Arg repeat, mediate high avidity binding to DNA, as exemplified by resistance to detergent extraction. Our findings identify high avidity binding to DNA as a portable inhibitory signal that counteracts proteasomal degradation.