Preheat the oven to 400˚F. Line a baking sheet with aluminum foil.
Place the chicken on a cutting board with the smooth side down. Cut a few long slits on the thick part of the meat (do not cut through, just about halfway down into the meat), so the meat has about the same thickness when lay flat. Place onto the baking sheet. Rub with a little bit of olive oil. Season lightly with salt and pepper on both sides. Bake in the oven for 15 – 20 minutes, or juices run clear when cut into the thickest part. Remove from oven. Transfer the chicken to a large plate to cool to room temperature, about 20 minutes.
In a large bowl, combine Greek yogurt and mayonnaise. Stir in tarragon. Season with 1/8 teaspoon salt and ¼ teaspoon pepper. Cover with plastic wrap. Return to the fridge to keep cool.
Lay about 6 – 7 butter lettuce leaves on each plate.
When the chicken is cool, cut into ¾-inch cubes. Add to the yogurt mixture. Toss in grapes. Mix well. Taste and adjust seasoning. Divide the chicken salad to the plates of lettuces. Serving immediately.