Heat the oil in a frying pan over medium high heat and cook the tenderloins until lightly golden and just cooked through. Remove from pan and set aside to cool.
When cool - shred chicken
In a bowl, gently stir together cream cheese, blue cheese, apple, walnuts, juice and tarragon
Spread a generous amount of blue cheese spread onto the slices of rye, top with chicken. Garnish with tarragon