No. The viruses were probably the second. You need some form of self replicating metabolism, before having a virus to be able to feed on it.
I would imagine the earliest forms of life (proto-life if we use cellular structure in the definition of life) were free-floating strands of genetic material, more similar to viruses than to fully formed cells. Or if that's on the right track, we could say the first "cells" were large bowls of the primordial soup.
Take a look at the videos at this link. (the ones showing the fatty acids holding onto each other)