Put hazelnuts in an 8- to 9-inch square baking pan. Bake in a 350° regular or convection oven until nuts are golden beneath skins, 12 to 15 minutes. Pour from pan onto a towel. When cool enough to handle, rub nuts in towel to remove loose skins. Lift nuts from towel and coarsely chop; discard skins.
Rinse chicken and pat dry. Place each breast between two sheets of plastic wrap. With a flat mallet, gently pound to about 1/2 inch thick. Peel off plastic and sprinkle chicken lightly on both sides with salt and pepper.
Heat oil in a 10- to 12-inch frying pan over medium-high heat; when hot, add chicken and turn occasionally until pieces are lightly browned on both sides and no longer pink in the center (cut to test), 6 to 8 minutes total. Transfer to a plate and cover with foil to keep warm.
Meanwhile, rinse, peel, and core pear and apple; cut each lengthwise into 8 wedges. Add butter and brown sugar to frying pan; stir over medium-high heat until butter is melted and sugar is dissolved, about 1 minute. Add fruit and stir often until beginning to brown, 2 to 3 minutes. Stir in vinegar and orange juice, bring to a boil, and stir often until fruit is tender when pierced and liquid is slightly thickened, 8 to 10 minutes.
Divide salad greens equally between two dinner plates and set a chicken breast half on each mound. Spoon hot fruit and liquid over chicken and greens. Sprinkle evenly with toasted hazelnuts and blue cheese. Add more salt and pepper to taste.