I heard someone say that God loves us with grace and then defined grace as "undeserved love."
In a day and age when so many are feeling worthless and unloved, how is it an encouragement to be loved, in spite of yourself? We are human. We aren't perfect, we all make mistakes... Does that make us undeserving?
I think that the brokeness of the human condition only makes us more in need of unconditional love. If God is going to dole out love as a show of how gracious he is, then he can keep it.