Carry each other's burdens, and in this way you will fulfill the law of Christ.
But what is that law of Christ?
The context of the surrounding letter to Galatia indicates that it can't be another set of laws, commandments, rules, and amendments. There was nothing wrong with the law God originally gave - except that it couldn't save anyone.
And the first phrase in that verse indicates that this law must be social in nature, because fulfilling it is achieved by carrying each other's burdens.
I'll tell you what I believe the law of Christ is.
One of the teachers of the law came and heard them debating. Noticing that Jesus had given them a good answer, he asked him, "Of all the commandments, which is the most important?"
"The most important one," answered Jesus, "is this: 'Hear, O Israel, the Lord our God, the Lord is one. Love the Lord your God with all your heart and with all your soul and with all your mind and with all your strength.' The second is this: 'Love your neighbor as yourself.' There is no commandment greater than these."
"Well said, teacher," the man replied. "You are right in saying that God is one and there is no other but him. To love him with all your heart, with all your understanding and with all your strength, and to love your neighbor as yourself is more important than all burnt offerings and sacrifices."
When Jesus saw that he had answered wisely, he said to him, "You are not far from the kingdom of God." And from then on no one dared ask him any more questions. ~ Mark 12:28-34, emphasis mine
In Luke's account, the teacher of the law who had it almost all figured out, almost spoiled it by trying to justify himself and asked, "And who is my neighbor?" So, gently, Jesus tells him a story about a traveler and some thieves and a priest and a Levite and a Samaritan - a very, very good Samaritan.
This is the law that Christ embodied, and when that body was taken and beaten and stripped and tortured and crucified, He embodied it all over again.
It is the law of Christ because it far predated the teacher of the law who commended it. It was from God, and John tells us that He was with God from the beginning. God emphasized it by repeating the first part five times in Deuteronomony alone (6:5, 10:12, 11:13, 13:3, and 30:31). The second part is Leviticus 19:18, and a huge chunk of the surrounding 613 precepts of the law are devoted to teaching how one should and should not express that love. With regard to this second one, Paul tells the Romans (13:9) that:
The commandments, "Do not commit adultery," "Do not murder," "Do not steal," "Do not covet," and whatever other commandment there may be, are summed up in this one rule: "Love your neighbor as yourself."
And in Matthew's account of a similar test question from Pharisees and teachers of the law, Jesus answers with both these fundamental precepts, and adds:
"All the Law and the Prophets hang on these two commandments."
You can list all of the other imperatives Jesus ever uttered, and weed out the ones that were specific to certain people or circumstances ("Go into the city and find a man with a donkey") and call them commands all you want to - but they're not. They will naturally fall, however, under one or both of these commandments.
Because it flows from the heart. It is the expression of devotion to God and love for others. Nothing else is regarded as a commandment in that attitude and mindset; it is an opportunity to imitate Christ, a blessing to be able to serve and give sacrificially as He gave; a gift of His Holy Spirit that empowers one to be a partner with God in Christ to do good works and to share this incredible, life-changing story.
Law can't save. Commandments can't save. You break one, you break the whole thing. If you look at everything imperative as a commandment, you have to do it or not do it. It's no longer an "I get to" but an "I have to."
"Give to the poor" but "You will always have the poor with you."
And you can't. You can't do all of the things you perceive are commanded, or not do all of the things you perceive are forbidden.
So law and commandments lead to helplessness and hopelessness, but
Thanks be to God—through Jesus Christ our Lord!
That is not what He came to bring.
He came to bring opportunity, and empowerment, and freedom to be a channel of them to the blessing of others and the glory of God.
And if we see everything imperative with that setting of mind-and-heart-and-soul-and-strength, we are no longer limited by what is "authorized" by a "law of silence" somehow hidden deep in the bowels of scripture that God supposedly put there to make it more difficult to share the gospel in far-flung lands or help orphans or worship our Lord together.
Jesus came to our world to bring fulfillment to law; and something much more important, more vital, more capable of saving us than law could ever be:
"For the law was given through Moses; grace and truth came through Jesus Christ." ~ John 1:17