Preheat oven to 400 degrees F.  

Put the potatoes on a sheet pan and bake for 30 minutes. Remove from oven, prick with a fork and continue baking another 30 minutes or so, until a knife slides into the potatoes with no resistance. Remove and let cool slightly. 

While potatoes are baking, combine the basil, garlic, walnuts, and oil in a blender or food processor and pulse until blended.  

Transfer to a bowl and add a pinch of salt and pepper, and add the chicken. Mix well.  

Split the potatoes open and stuff with the chicken mixture.  

Serve immediately.