Fill a large pot halfway with water and bring to a boil. Prepare an ice bath nearby. Add beans to pot and reduce heat to medium-high. Cook until tender-crisp, about 5 minutes. Drain and plunge into ice bath; drain again and set aside.
In a large nonstick skillet, heat 1 tsp oil on medium. Add mushrooms and sauté, stirring occasionally, for 8 to 10 minutes. Stir in garlic, lemon zest and juice and sauté for 1 minute. Stir in beans and heat through. Remove from heat and cover to keep warm.
Meanwhile, in a separate large nonstick skillet, heat remaining 1 tsp oil on medium. Add onion and sauté for 5 minutes. Add chicken, vinegar, thyme and salt and cook, stirring often, for 8 minutes, until chicken is cooked through. Remove from heat. Divide chicken and bean mixtures among plates and drizzle chicken with pan juices.
Serving Size: 4 oz chicken mixture and 7 oz mushroom mixture