The majority of emerging zoonoses originate in wildlife, and many are caused by viruses. However, there are no rigorous estimates of total viral diversity (here termed “virodiversity”) for any wildlife species, despite the utility of this to future surveillance and control of emerging zoonoses. In this case study, we repeatedly sampled a mammalian wildlife host known to harbor emerging zoonotic pathogens (the Indian Flying Fox, Pteropus giganteus) and used PCR with degenerate viral family-level primers to discover and analyze the occurrence patterns of 55 viruses from nine viral families. We then adapted statistical techniques used to estimate biodiversity in vertebrates and plants and estimated the total viral richness of these nine families in P. giganteus to be 58 viruses. Our analyses demonstrate proof-of-concept of a strategy for estimating viral richness and provide the first statistically supported estimate of the number of undiscovered viruses in a mammalian host. We used a simple extrapolation to estimate that there are a minimum of 320,000 mammalian viruses awaiting discovery within these nine families, assuming all species harbor a similar number of viruses, with minimal turnover between host species. We estimate the cost of discovering these viruses to be ~$6.3 billion (or ~$1.4 billion for 85% of the total diversity), which if annualized over a 10-year study time frame would represent a small fraction of the cost of many pandemic zoonoses.