Loving Obedience
The law requires parents to feed and clothe their children. But do you think parents care for their children because the law requires it? Of course not! They do it because they love them. When you truly love someone, fulfilling the law is no problem. In fact, you're likely to go way beyond the law in showing your love.
It's the same thing with loving God. Maybe you serve Him because you're trying to gain His favor, or because you think His law requires it. But shouldn't the real reason be because you love Him? Truth is, your motives will determine whether you are living under grace or some form of legalism.
Sure, you can serve God out of a sense of duty or obligation, but there's a good chance you'll be missing out on the joy of serving purely out of love.