COVID-19, the illness caused by infection with the novel coronavirus SARS-CoV-2, is a rapidly spreading global pandemic in urgent need of effective treatments. Here we present a comprehensive examination of the host- and virus-targeted functions of the flavonolignan silibinin, a potential drug candidate against COVID-19/SARS-CoV-2. As a direct inhibitor of STAT3—a master checkpoint regulator of inflammatory cytokine signaling and immune response—silibinin might be expected to phenotypically integrate the mechanisms of action of IL-6-targeted monoclonal antibodies and pan-JAK1/2 inhibitors to limit the cytokine storm and T-cell lymphopenia in the clinical setting of severe COVID-19. As a computationally predicted, remdesivir-like inhibitor of RNA-dependent RNA polymerase (RdRp)—the central component of the replication/transcription machinery of SARS-CoV-2—silibinin is expected to reduce viral load and impede delayed interferon responses. The dual ability of silibinin to target both the host cytokine storm and the virus replication machinery provides a strong rationale for the clinical testing of silibinin against the COVID-19 global public health emergency. A randomized, open-label, phase II multicentric clinical trial (SIL-COVID19) will evaluate the therapeutic efficacy of silibinin in the prevention of acute respiratory distress syndrome in moderate-to-severe COVID-19-positive onco-hematological patients at the Catalan Institute of Oncology in Catalonia, Spain.