If the definition of life is that it must be made of cells, then the answer is no, because viruses are not surrounded by a cellular membrane. However, perhaps it is time to revisit the definition of life, because viruses can certainly act like living organisms. It is true that they are parasitic and cannot function outside of a host cell, but once they have invaded that cell, they are capable of reproduction, which is something that only living organisms can do.
What viruses share with all living organisms is the presence of the genetic molecules, DNA and RNA. In fact viruses are little more than DNA wrapped in a protein coat. Perhaps the definition of life should be extended to nucleic acids because they are the only self- replicating molecules. Perhaps life began when the first self-replicating molecules evolved in the primordial soup. The simplest cells are just packages for the replicating molecules: protein packages that protect those molecules, with the formulas for the proteins coming from the DNA instructions.
The beginnings of life have always been mysterious. For many, it was the sticking point for the theory of evolution. How could life come into existence in the first place? The experiments of Urey and Miller conducted in 1952 showed that complex organic molecules such as nucleic acids and proteins could form in the conditions thought at the time to be present in the early history of the earth. There has been some controversy over the actual nature of the early atmosphere, but other experiments under reducing atmospheric conditions also produced nucleic acids and proteins. Once these nucleic acids formed and began self-reproducing, it could be said that a state of proto-life existed.
So is this what viruses are? A form of proto-life? It is true that they are dormant outside of a host cell. But once they have penetrated that cell, which they are fully capable of doing, they come to life in a way that is now described as virulent. Virulent comes from the word virus and describes the devastating effects that a viral infection can have on its host. The virus uses its DNA to change the host cells to mass producers of new viruses. From the common cold to small pox to AIDS, viruses have caused biological havoc in millions of human beings. Is this the work of a non-living organism? I don't think so. Simple as they are, lacking a cellular membrane as they are, they still satisfy this most basic function of life: they can reproduce very effectively.