Viral infections are one of the major causes of death worldwide, with HIV infection alone resulting in over 1.2 million casualties per year. Antiviral drugs are now being administered for a variety of viral infections, including HIV, hepatitis B and C, and influenza. These therapies target a specific phase of the viruss life cycle, yet their ultimate success depends on a variety of factors, such as adherence to a prescribed regimen and the emergence of viral drug resistance. The epidemiology and evolution of drug resistance have been extensively characterized, and it is generally assumed that drug resistance arises from mutations that alter the viruss susceptibility to the direct action of the drug. In this paper, we consider the possibility that a virus population can evolve towards synchronizing its life cycle with the pattern of drug therapy. The periodicity of the drug treatment could then allow for a virus strain whose life cycle length is a multiple of the dosing interval to replicate only when the concentration of the drug is lowest. This process, referred to as drug tolerance by synchronization, could allow the virus population to maximize its overall fitness without having to alter drug binding or complete its life cycle in the drugs presence. We use mathematical models and stochastic simulations to show that life cycle synchronization can indeed be a mechanism of viral drug tolerance. We show that this effect is more likely to occur when the variability in both viral life cycle and drug dose timing are low. More generally, we find that in the presence of periodic drug levels, time-averaged calculations of viral fitness do not accurately predict drug levels needed to eradicate infection, even if there is no synchronization. We derive an analytical expression for viral fitness that is sufficient to explain the drug-pattern-dependent survival of strains with any life cycle length. We discuss the implications of these findings for clinically relevant antiviral strategies.