In (+) RNA coronaviruses, replication and transcription of the giant ∼30 kb genome to produce genome‐ and subgenome‐size RNAs of both polarities are mediated by a cognate membrane‐bound enzymatic complex. Its RNA‐dependent RNA polymerase (RdRp) activity appears to be supplied by non‐structural protein 12 (nsp12) that includes an RdRp domain conserved in all RNA viruses. Using SARS coronavirus, we now show that coronaviruses uniquely encode a second RdRp residing in nsp8. This protein strongly prefers the internal 5′‐(G/U)CC‐3′ trinucleotides on RNA templates to initiate the synthesis of complementary oligonucleotides of <6 residues in a reaction whose fidelity is relatively low. Distant structural homology between the C‐terminal domain of nsp8 and the catalytic palm subdomain of RdRps of RNA viruses suggests a common origin of the two coronavirus RdRps, which however may have evolved different sets of catalytic residues. A parallel between the nsp8 RdRp and cellular DNA‐dependent RNA primases is drawn to propose that the nsp8 RdRp produces primers utilized by the primer‐dependent nsp12 RdRp.