Hello gina, I think the key to your problem may be in the word "old" that you used to describe your chestnut tree.
Our garden is riddled with honey fungus but I've found that the plants that fall victim to it are generally old or in some way weakened. Also, I've found that by avoiding deep cultivation of the soil around shrubs I lessen the chances of scratching the host plants' roots and the fungus getting a foothold in the hosts' root systems.
Plants that die are best removed as completely as possible. I then sometimes plant a new plant in the same site but first put it in a bottomless bucket filled with compost. This gives the new plant a chance to put its roots down first into clean compost and later more deeply into the soil below the level of the bootlaces.
Just a theory I have. I don't know if other people have tried that.