What is the best way for me to lay hardwood around my masonry fireplace hearth? As you can see in the pictures, if I undercut the cut will be right into the mortar. Will the mortar cut smoothly or will it chip leaving a "ragged edge" above the wood?

http://pixupload.com/public/viewset/71

You will need two cuts on this one... one flush with the subfloor and then the higher cut. If you got a good blade it should not chip when cutting. Chiseling out the meat is where you will have to be real careful and not try to pry up against that top cut. Just go slow... and make that top cut just slightly higher than the wood.

Not real good pictures here, but you get the idea http://www.custom-surfaces.com/23.html

Sometimes it is brittle and the mortar will shear off. They have sanded caulking that is color matching to colored grout. The light gray, matches most brick mortar.

So undercut is the best way to go in my situation? How far in should I make the cut and then how much space should I leave between the edge of the board and the uncut brick/mortar?

An inch or a little more of undercut, works for me.

That's an interesting floor/fireplace junction. It looks like the fireplace went in before the subfloor. On mine, the subfloor was in first and the bottom layer was all mortar. I was able to chisel out up to the the bottom of the first brick, just right for my 1/2" flooring.

I agree that about an inch back is enough. You want to be able to get the flooring in far enough so that you cannot see the end of it when standing back and looking at where the flooring meets the brick.