Water Trickling From Ice Dispenser?

We have a GE side by side with ice/water dispenser. The ice started getting stuck and not coming out. I discovered there was a large frozen piece of ice inside the door where the ice comes out. I removed this chunk. It's forming again and there is a tiny trickle of water behind the ice dispenser lever on the outside of the door in the ice/water dispenser box. We can not find where it is coming from. Any ideas for simple fix?