The lymphocytic choriomeningitis virus (LCMV) is a non-cytopathic virus broadly used in fundamental immunology as a mouse model for acute and chronic virus infections. LCMV remains a cause of meningitis in humans, in particular the fatal LCMV infection in organ transplant recipients, which highlights the pathogenic potential and clinical significance of this neglected human pathogen. Paradoxically, the kinetics of the LCMV intracellular life cycle has not been investigated in detail. In this study, we formulate and calibrate a mathematical model predicting the kinetics of biochemical processes, including the transcription, translation, and degradation of molecular components of LCMV underlying its replication in infected cells. The model is used to study the sensitivity of the virus growth, providing a clear ranking of intracellular virus replication processes with respect to their contribution to net viral production. The stochastic formulation of the model enables the quantification of the variability characteristics in viral production, probability of productive infection and secretion of protein-deficient viral particles. As it is recognized that antiviral therapeutic options in human LCMV infection are currently limited, our results suggest potential targets for antiviral therapies. The model provides a currently missing building module for developing multi-scale mathematical models of LCMV infection in mice.