Season chicken with salt and pepper. Heat oil in a grill pan over medium-high heat. Add chicken and brown on both sides, 10-12 minutes total. Transfer to a plate.
Add chicken broth to hot skillet using a wooden spoon to scrape bits from pan. Pour into a small bowl and set aside to cool for 5 minutes, then whisk in Chobani, mustard, tarragon and a pinch of salt and pepper. Serve over chicken.