Heat the olive oil in a large sauté pan over medium-high heat. Season chicken breasts with salt and pepper, lightly dredge them in all-purpose flour (shaking off any excess), and then carefully place them in the skillet. Cook until chicken breasts are golden and nearly cooked through, about 5 minutes per side. Transfer to a plate, and cover.
In the same pan, sauté the shallots over medium heat until tender, about 1 minute. Add white wine, and use a wooden spoon to scrape any browned bits from the bottom of the pan. Simmer 1 minute, stirring constantly. Add the chicken broth; simmer, covered, over medium-low heat 5 minutes.
Return chicken breasts to the pan, and cook over medium heat 4 minutes or until cooked through. Remove the chicken breasts, and place 1 breast on each of 4 plates. Stir the tomatoes and tarragon into the broth mixture; pour 1/3 cup sauce over each chicken breast. Sprinkle with cheese, and serve warm.