Grace = Fear???

Ever sang the song "Amazing Grace"? I have many times but this last week something struck me as I sang again. In one of the verses there are two line that stood out and I just can't let it go. They go something like this: "twas grace that taught me heart to fear, and grace my fears released." The second line makes perfect sense but grace teaching fear seems a bit odd and hard to comprehend. How does getting what we don't deserve cause us to fear? Is it that we are given so much and it is hard to handle? I wonder what the writer really meant when they coined those words. It is good to think about. The better I can understand Grace, God's Grace, the better I will be at living it out.