This is a good question, but "virtuous" is ultimately a term going back to one's definition of good and bad.
Your virtue will do me good, and do others good, and do you some good, too.
But will the quality of your virtue be found sufficient in God's eyes to consider his son's sacrifice for your sin pointless?
"All these [commandments] I have kept," the young man said. "What do I still lack?" Jesus answered, "If you want to be perfect, go, sell your possessions and give to the poor, and you will have treasure in heaven. Then come, follow me." When the young man heard this, he went away sad, because he had great wealth.
- Matthew 19:20-22
"Is religion necessary to live a virtuous life?"
Vir-tu-ous: Exhibiting virtue.
Vir-tue: Moral excellence and righteousness
Re-lig-ion: Belief in and reverence for a supernatural power…
My answer is a tentative no. I think atheists can exhibit moral excellence, but of course there is the question of how is one measuring their character - excellent according to whose standards? There is only one standard that matters, and that's God's.
Consider Jesus' example of the rich young ruler. That was an example of someone living a virtuous life. But Jesus was able to suggest something to him which resulted in the man's true lack of selflessness being exposed. Perhaps the young man was very, very virtuous, but he wasn't perfectly virtuous. He was not up to God's standards. Don't misunderstand, virtue is commendable, it just isn't reliable; that is, don't rely on merely a high degree of virtue to get you into heaven. Our personal standards don't mix well with God
Chemically speaking, if you take a pure substance "A" and mix with it any other substance "non-A", then your resulting mix is no longer pure. Concerning God and us, God is pure, and we can be very virtuous; but we cannot be perfectly virtuous, we cannot be perfectly pure. Therefore we cannot be allowed to contaminate God's presence if he is to remain pure. Unless and until our impurity is dealt with, we will not be compatible to join God in heaven.
If you're living a virtuous life, that does the rest of us much good, really; but come the judgment it won't be enough to do you sufficient good as to make Jesus say "You didn't need me." Your virtuous life might make me comfortable as a citizen of this world; but believing myself to also be a citizen of the next, I can tell you your virtue won't accomplish for you all that you expect. If this describes you, may you someday take hold of the inheritance of virtue and righteousness that is in Christ.
Malice toward none and charity for all?
What is religion?