Viruses have evolved to efficiently direct the resources of their hosts toward their own reproduction. A quantitative understanding of viral growth will help researchers develop antiviral strategies, design metabolic pathways, construct vectors for gene therapy, and engineer molecular systems that self-assemble. As a model system we examine here the growth of bacteriophage T7 in Escherichia coil using a chemical-kinetic framework. Data published over the last three decades on the genetics, physiology, and biophysics of phage T7 are incorporated into a genetically structured simulation that accounts for entry of the T7 genome into its host, expression of T7 genes, replication of T7 DNA, assembly of T7 procapsids, and packaging of T7 DNA to finally produce intact T7 progeny. Good agreement is found between the simulated behavior and experimental observations for the shift in transcription capacity from the host to the phage, the initiation times of phage protein synthesis, and the intracellular assembly of both wildtype phage and a fast-growing deletion mutant. The simulation is utilized to predict the effect of antisense molecules targeted to different T7 mRNA. Further, a postulated mechanism for the down regulation of T7 transcription in vivo is quantitatively examined and shown to agree with available data. The simulation is found to be a useful tool for exploring and understanding the dynamics of virus growth at the molecular level.