In a large bowl, whisk together 1 tablespoon olive oil, 1 tablespoon vinegar and 1 teaspoon mustard; season with salt and pepper. Add the orange segments.
Season the chicken with salt and pepper. In a large nonstick skillet, heat the remaining 2 tablespoons olive oil over medium-high heat. Add the chicken and cook, turning once, until golden and cooked through, 12 to 15 minutes; transfer to a plate and cover to keep warm.
Lower the heat to medium and add the remaining 1 tablespoon vinegar to the pan, scraping up any browned bits. Whisk in the cream, the remaining 2 tablespoons mustard and the tarragon and cook until slightly thickened, about 1 minute.
Add the lettuce to the orange mixture and toss to coat. Slice the chicken against the grain 1/2 inch thick and divide among 4 plates. Spoon the sauce over the chicken and serve with the salad.