I can't believe I didn't post this back in 2013 when I was faced with gutters filled with frozen ice. I tried chipping out the ice to no avail. I tried using a small blowtorch (a really dumb idea) and got nowhere. A little Internet searching provided some hope, but it didn't seem possible, which fortunately didn't stop me from trying. As per the directions at the link below, I bought a pair of pantyhose, cut off the waist, filled a leg with calcium chloride driveway salt, and laid it on top of a section of frozen gutter. The next morning I got back up on the ladder and to my complete surprise, that section of gutter was completely clear of ice. Bought more pantyhose, more salt and repeated the process and by the next day, the gutters were all clear.