Giant viruses are a recently-discovered (2003) group of viruses, some of which have a genome larger than that of many bacteria. Their evolutionary history is a mystery.

The discovery of giant viruses blurred the sharp division between viruses and cellular life. Giant virus genomes encode proteins considered as signatures of cellular organisms, particularly translation system components, prompting hypotheses that these viruses derived from a fourth domain of cellular life."

Source : Science

One theory suggests they may have evolved from smaller viruses.

Their discovery and subsequent characterization has triggered some debate concerning the evolutionary origins of giant viruses. The two main hypotheses for their origin are that either they evolved from small viruses, picking up DNA from host organisms, or that they evolved from very complicated organisms into the current form which is not self-sufficient for reproduction. What sort of complicated organism giant viruses might have diverged from is also a topic of debate. One proposal is that the origin point actually represents a fourth domain of life, but this has been largely discounted. ^{[see ref. above]}

Source : Wikipedia

Note: Another group of virus-like entities called virophages are parasitic, possibly symbiotic, within the Giant Viruses. They were first discovered in a power-plant cooling tower, in 2008. Their evolutionary origin is also unknown.