This song is played on just about every Hollywood movie that features soldiers. It's truly a beautiful, timeless melody that is probably known around the world.
Here is an easy guitar arrangement of the song that allows you to play both the chords and the melody. There are a few bluesy licks in there to add a little flair to it, but it sticks to the chords and melody pretty close.
You can also download the PDF of the arrangement: Amazing Grace Guitar Arrangement PDF