2+ years after we purchased the house, we have completely rid the property of the old chain-link fencing. Below is a shot of the last remaining panel as of yesterday morning, 8am. I had already removed the panel & post that went down the hill to the sidewalk.
By 9am I had removed the actual fencing and the post at the top of the hill. As that post was at the top of the hill, I could just dig into the hill to reach the concrete and then pull it out. Mighty heavy, but it didn't require my usual technique: the sledge-hammer. Seriously, provided you don't need to be certain of getting all of the concrete base out, a sledge hammer works wonders. Dig around the post base some, then wail away. It will either loosen up the whole post so you can pull it and its base up, or it will crack the concrete base so you can pull up the post itself. OK, so it's not quiet, and it does dent the posts so they aren't very usable, but I doubt many people plan on re-using old chain-link posts.