Viral infection relies on the hijacking of cellular machineries to enforce the reproduction of the infecting virus and its subsequent diffusion. In this context, the replication of the viral genome is a key step performed by specific enzymes, i.e., polymerases. The replication of SARS-CoV-2, the causative agent of the COVID-19 pandemics, is based on the duplication of its RNA genome, an action performed by the viral RNA-dependent RNA polymerase. In this contribution, by using highly demanding DFT/MM-MD computations coupled to 2D-umbrella sampling techniques, we have determined the chemical mechanisms leading to the inclusion of a nucleotide in the nascent viral RNA strand. These results highlight the high efficiency of the polymerase, which lowers the activation free energy to less than 10 kcal/mol. Furthermore, the SARS-CoV-2 polymerase active site is slightly different from those usually found in other similar enzymes, and in particular, it lacks the possibility to enforce a proton shuttle via a nearby histidine. Our simulations show that this absence is partially compensated by lysine whose proton assists the reaction, opening up an alternative, but highly efficient, reactive channel. Our results present the first mechanistic resolution of SARS-CoV-2 genome replication at the DFT/MM-MD level and shed light on its unusual enzymatic reactivity paving the way for the future rational design of antivirals targeting emerging RNA viruses.