In a small bowl, mix mustard, maple syrup, olive oil and tarragon. Add salt and pepper. Brush each slice of pear with a little bit of this mustard mixture. Put 3 slices on a baking sheet, overlapping them slightly. Do the same with the remaining slices. Set aside.
In a bowl, pour remaining of mustard mixture, add chicken and stir to coat well. In a large non-stick skillet, cook chicken at medium heat 4 to 6 minutes or until golden (flip it at mid-cooking). Put chicken breasts on the bed of sliced pears. Cook in a preheated oven of 350 F for 15 to 18 minutes or until chicken is not pink inside.
Meanwhile, pour chicken stock in the skillet and scrape the bottom with a wood spoon and cook at medium heat 3 to 5 minutes or until the sauce has reduced to a third.
When ready to serve, distribute the bed of pears and chicken breasts in the plates and sprinkle with a little bit of sauce.