Though I didn't mention it, I'm already doing this. Using a heavy shovel and a digging fork, I've been prying up one end of the concrete and putting a rock underneath it, a few inches back from the end, so that the concrete is unsupported at the end and stresses in the concrete are concentrated around the rock. Without that, I would have gotten nowhere with the hammer and chisel.
It seems the most common recommendation is to just get a bigger hammer and hit the concrete with it directly, forgetting about the chisel. So I think I'll try that.
Thanks for all the suggestions!
Dave