Looks like the beginning of botrytis, which is a pretty severe fungal condition that affects peonies. Read up on it here.

Thanks, gardengal. We have had quite a bit of rain here lately. I hope if I remove the infected area it won't spread to the rest of the plant or the other peonies surrounding this one. How far down below the fungus do you suggest that I cut? Is 6 inches enough or too much? Thank you again!

Just take off as much as looks impacted, don't need to go down into the healthy parts unless they start looking bad.

Thank you, Liz. I removed to the next leaf set