Brush the chicken with 2 tablespoons olive oil; season with salt and pepper. Heat a grill pan over medium heat; add the chicken, cover and cook, turning, until cooked through, about 12 minutes. Let cool, then thinly slice.
In a large bowl, whisk together the remaining 3 tablespoons olive oil, the vinegar, tarragon, shallot, lemon juice and mustard; season with salt and pepper. Add the chicken, greens, grapes and hazelnuts; toss to coat.