Make marinade: combine chicken breast, lemon juice, oil, wine, 2 teaspoons of the rosemary, shallot, salt, and pepper in a zip-top plastic bag or marinade dish. Mix well and seal. Let marinate at least 2 hours.
Drain the marinade into a medium skillet, reserving chicken. Heat marinade over medium-high heat. Sauté the chicken breasts in the marinade, turning once or twice, until lightly browned.
Reduce heat, cover chicken with the green beans and chicken broth. Cover pan and simmer until chicken is tender and green beans cooked, about 5-7 minutes.
Remove chicken and green beans to serving plates. Heat remaining sauce to a boil and reduce slightly. Remove from heat. Stir in the butter to thicken the sauce. Serve sauce over chicken and green beans. Sprinkle with the remaining teaspoon of rosemary.