Paul starts of his discussion in this chapter by discussing freedom. More specifically, freedom throuch Christ our Lord, a theme that runs through the chapter (and the entire Bible). Through Christ, we are no longer slaves to sin (taken further, when we are in Christ, we are no longer trying to serve two masters). We are no longer slaves to sin and death because, "Those who belong to Christ Jesus have crucified the sinful nature with its passions and desires," (v. 24).
Being free in Christ means we can no longer (and no longer have to) make OURSELVES holy. We are no longer dependant on following the Law for salvation (Paul lifts up circumcision as an example). Instead, we are saved by Grace through faith in the blood of Christ.
What does it look like to be in Christ, then? Paul says, "The only thing that counts is faith expressing itself through love," (v. 6) (I see Martin Luther King as an example of faith in Love). He says to serve one another in Love. He then repeats Christ in summing up the Law, which we will follow not for salvation's sake, but in the name of Love (as God is Love). "Love your neighbor as yourself." In fact, the Gospel is so good because of the news in it: God loves us. It is a challenge to apply, though, because God wants us to love him.
Post Script: And yes, I am listening to U2 as I type this.