Herpesviruses are known to encode a number of inhibitors of host cell death, including RIP Homotypic Interaction Motif (RHIM)-containing proteins. Varicella zoster virus (VZV) is a member of the alphaherpesvirus subfamily and is responsible for causing chickenpox and shingles. We have identified a novel viral RHIM in the VZV capsid triplex protein, open reading frame (ORF) 20, that acts as a host cell death inhibitor. Like the human cellular RHIMs in RIPK1 and RIPK3 that stabilise the necrosome in TNF-induced necroptosis, and the viral RHIM in M45 from murine cytomegalovirus that inhibits cell death, the ORF20 RHIM is capable of forming fibrillar functional amyloid complexes. Notably, the ORF20 RHIM forms hybrid amyloid complexes with human ZBP1, a cytoplasmic sensor of viral nucleic acid. Although VZV can inhibit TNF-induced necroptosis, the ORF20 RHIM does not appear to be responsible for this inhibition. In contrast, the ZBP1 pathway is identified as important for VZV infection. Mutation of the ORF20 RHIM renders the virus incapable of efficient spread in ZBP1-expressing HT-29 cells, an effect which can be reversed by the inhibition of caspases. Therefore we conclude that the VZV ORF20 RHIM is important for preventing ZBP1-driven apoptosis during VZV infection, and propose that it mediates this effect by sequestering ZBP1 into decoy amyloid assemblies.