A high moral standard unobtainable by unbelievers?

I was reading through my Major Bible Themes book (Lewis Sperry Chafer) and I ran across a quote that threw me for a loop.

"The death of Christ assures us of the love of God towards the sinner" (John 3:16; Rom. 5:8; I John 3:16; 4:9)

I know this, and it is easy to understand, but the next line...

"The fact that God loves us should influence believers in Christ to live on a high moral standard impossible for an unbeliever" (2 Cor. 5:15; I Pet. 2:11-25)

I'm a believer in Christ. Do I live on a high moral standard impossible for an unbeliever? Do we even believe, as Christians, that there is a high moral standard that we can obtain in Christ that unbelievers cannot ever reach alone? I think in a way this is a simple concept, but the phrasing cast a different approach, at least for me, to living a life that radiates Christ.