Aicardi-Goutières syndrome (AGS) is a genetically determined early-onset progressive encephalopathy caused by mutations leading to overexpression of type I interferon (IFN) and resulting in various clinical phenotypes. A gain-of-function (GOF) mutation in the gene is associated with robust production of type I IFN and activation of the Janus kinase (JAK) signal transducer and activator of the transcription (STAT) pathway, which can cause AGS type 7. We detail the clinical case of an infant who initially presented with pneumonia (PCP), had recurrent respiratory infections, and was later treated with a JAK inhibitor, baricitinib, because of a genetically confirmed GOF mutation in the gene. This spectrum of GOF mutations with overlapping features of hyperinflammation and severe opportunistic infection, which mimics combined immunodeficiency (CID), has not been described before. In this case, therapy with baricitinib effectively blocked IFN-α activation and reduced STAT1 signaling but had no effect on the progression of the neurological disease.