Viruses express proteins with silencing suppression activity to counteract the RNA silencing-mediated defense response of the host. In the family Closteroviridae, examples of multiple-component RNA silencing suppression systems have been reported. To ascertain if this is a general strategy in this group of viruses, we have explored the bipartite genome of Tomato chlorosis virus (ToCV, genus Crinivirus). We have identified the RNA1-encoded p22 protein as an effective silencing suppressor by using a Agrobacterium co-infiltration assay. p22 suppressed local RNA silencing induced either by sense RNA or dsRNA very efficiently, but did not interfere with short or long-distance systemic spread of silencing. We have also demonstrated by using the heterologous vector PVX the silencing suppression activity of the RNA-2 encoded coat protein (CP) and minor coat protein (CPm). In this study, we demonstrate an even greater complexity of silencing suppressor activity for a plant virus, and for the first time we show the presence of RNA silencing suppressor genes encoded by both genomic RNA molecules of a bipartite genome in the complex family Closteroviridae.