Cream the butter in a bowl with the lemon rind and tarragon. Season to taste with salt, pepper and lemon juice. Shape butter into a rectangular block, wrap in plastic and leave in freezer to set solidly. Peel away chicken skin and flatten between sheets of plastic film, taking great care not to make any holes in the meat. Cut the hard butter into 4 pieces and place each in the center of the chicken fillet. Make sure the piece of butter isn't too large to be completely enclosed within the fillet. Fold the edges neatly and roll the fillet up tightly. Secure with fine string. Beat egg lightly and coat the chicken before coating evenly with bread crumbs, pressing them in thoroughly. Leave in refrigerator or freezer util coating has set.
Heat oil in a deep fryer or pan to 375F. Fry the chicken without crowding pan and lowering temperature, until golden brown. Do not allow the oil to get too hot, or the chicken will brown before it is cooked inside.
Drain on absorbent paper.