Recent history is punctuated by the emergence of highly pathogenic coronaviruses such as SARS- and MERS-CoV into human circulation. Upon infecting host cells, coronaviruses assemble a multi-subunit RNA-synthesis complex of viral non-structural proteins (NSP) responsible for the replication and transcription of the viral genome. Here, we present the 3.1 Å resolution structure of the SARS-CoV NSP12 polymerase bound to its essential co-factors, NSP7 and NSP8, using single particle cryo-electron microscopy. NSP12 possesses an architecture common to all viral polymerases as well as a large N-terminal extension containing a kinase-like fold and is unexpectedly bound by two NSP8 co-factors. This structure illuminates the assembly of the coronavirus core RNA-synthesis machinery, provides key insights into NSP12 polymerase catalysis and fidelity and acts as a template for the design of novel antiviral therapeutics.