Rapidly labeled RNA was extracted from monkey cells after infection with Simian Virus 40 (SV40) and exposure to short pulses of [5-3H]uridine late in infection. When this RNA was self-annealed, it became resistant to digestion with ribonuclease. The fraction of RNA that resisted the ribonuclease treatment decreased with increased labeling time, or when a short pulse of radioactivity was followed by incubation with unlabeled uridine and actinomycin D. The RNase-resistant RNA was isolated by chromatography on Sephadex G-100 and shown to be double-stranded by its susceptibility to ribonuclease as a function of salt concentration and temperature. This behavior was not due to RNA-DNA hybrid formation, since deoxyribonuclease had no effect upon the double-stranded molecules, even after their denaturation. The relation of the double-stranded RNA to SV40 was demonstrated by the hybridization of about 50% (corrected value, >90%) of the separated RNA strands with component I of SV40 DNA from plaque-purified virus. After self-annealing in formamide at low temperature, about 10% of the rapidly labeled, viral RNA sedimented at 13 S. This value corresponds in size to about 60% of the SV40 DNA.