Shouldn't be an issue. In fact, if the tree has been dead a while and has started to rot, taking some off might get you down to more stable wood. I had a similar situation with a piece of standing dead cherry a while back.
Although, looking closer at the pic, kind of looks dark in the center which might be rot as well. Hard to tell from here in Maine.
Although, looking closer at the pic, kind of looks dark in the center which might be rot as well. Hard to tell from here in Maine.