Paul says: Only, live your life in a manner worthy of the gospel of Christ (Phil 1.27). What does this mean?
Some persons have the impression that the good news of Jesus Christ is merely that Christ has died for your sins in the sense that he has borne the punishment due to you; consequently God does not condemn you any longer and you are not under any obligation to impress God through works of the law or anything of the sort. If this is your conception of the good news of Jesus Christ, it may be difficult to see what "worthy" living might be. Isn't the whole point that I am not worthy, but Christ is for me? Why the attention to myself now?
I think the problem here is obviously with this understanding of the gospel of Jesus Christ, rather than with Paul's injunction. We can hardly suppose to know better than the apostle himself what his gospel entails and means.
Paul's gospel is certainly a message about what Christ has accomplished for me which I was unable to do myself. That much is certain. But it also contains a critical premise: that now, in virtue of what Christ has accomplished for me, my identity has changed, my place in the world is far different, and that now I am called to live into this new identity.
He says to the Colossians (my translation):
For it pleased God that the totality of things should dwell in [Christ], and through him to reconcile to Godself all things, making peace through the blood of the cross, both things on earth and in heaven. And you, though you were once estranged and hostile in mind, doing evil deeds -- now he has reconciled you in his physical body through death, to present you holy and blameless and irreproachable before God (1.19-22).
Notice that Paul speaks here of a changed reality for the Colossians which is localized in Christ's person: in Christ's body dwelt the whole totality of things created by Christ (πᾶν τὸ πλήρωμα; see v. 16), and all these things were reconciled to God through Christ's obedience unto death. This gospel naturally motivates the call to put aside one's false identity as sinner (see Col 3.9-10; Eph 4.22-4) and to adopt a new identity in Christ.
It is in this light that we ought to interpret "living worthily." If the good news is that Christ has reconciled me with God, and that in Christ I am in fellowship with God, then living worthily means living in a way that embodies this truth. If through Christ I have peace with God, then living worthily means living in peace with God -- not sinning, not opposing him, not hating him, not ascribing to him malevolence when things don't go as I'd hoped, living in obedience as Christ did, etc.
This is what it means to live worthily of the gospel. In a real way, living worthily gospel really means believing it, and showing that you believe it. If you believe that you are reconciled to God in Christ, why do you continue in sin? If you believe that in Christ you are the righteousness of God (cf. 2 Cor 5.21), why can't I tell a difference between you and the unbeliever in terms of your lifestyle?