Remove stalk, peel and slice persimmons into thin pieces. Combine the olive oil with the apple cider vinegar and set aside. Cut the fennel into thin shavings and add to the endive and dill. Combine the dressing through the greens.
Brush the chicken breast with olive oil and chargrill for 7 - 10 minutes each side. Allow to rest for 10 minutes before cutting into slices. and arrange on a platter with the chicken, remaining persimmon slices and toasted almonds. Season with black pepper and serve.
Note : Persimmons and Fuyi fruit are one and the same thing although they may be labeled separately in your green grocers.