Paul instructs the church in Galatia, “Bear one another’s burdens, and so fulfill the Law of Christ” (6:2). Protestant commentators, especially from the Lutheran tradition, often see this as a tongue-in-cheek paradox, as if inbetween the lines Paul is saying, “So, if you’re wanting to be enslaved to a law, go ahead and do this ‘law,’ foolish Galatians.” These Protestants contrast heavily the Law and the Gospel of faith without works – interpreted as without moral obligations. And if this was the only reference to the Law of Christ, then this would make a certain amount of sense. Paul elsewhere speaks of the Torah, or Mosaic Law, as something of a stopgap, holding things down until Christ appeared. At best, the Torah plays in Paul’s thought the necessary role of setting the scene and developing characters so that Christ’s entrance onto the stage of history makes sense.
There are a number of references to a “law of Christ,” “law of liberty,” or similar in several strands of the New Testament (e.g. Gal. 6:2; 1 Cor. 9:28; Jam. 1:25, 2:8). There’s enough similarity in contents that it’s very possible that a core of moral teachings for the New Covenant was recognized in the earliest Christian communities – a selection of Mosaic Laws recognized as still binding, the teaching of Christ (perhaps especially the group of sayings collected in the Sermon on the Mount), the example of Christ, and the Church’s experience of the Spirit’s work in their midst (Acts 10).
This makes sense especially given how the gospels portray Jesus. In each of the synoptic gospels (Matthew, Mark, and Luke), Jesus spends significant time discussing ethical issues. In Matthew especially, Jesus is the New Moses, giving a new Torah in the Sermon on the Mount. A key part of Jesus’ ministry is to form a certain kind of community among His followers with distinctive communal practices.
The New Covenant has a new Law but not a new legalism – as with the Mosaic Law, our salvation does not depend on our performance but on God’s graceful provision. But we are called to live out the Kingdom of God in the power of the Holy Spirit, to let our light shine before others that they may see our good works and give glory to our Father in heaven.