In a large skillet over medium high heat, warm the olive oil. Season the chicken, brown it in the oil for 2 or 3 minutes on each side, and remove to a plate.
Return pan to stove and reduce heat to medium. Add butter to the pan and saute the shallots, carrots, and mushrooms. Saute for 3 to 5 minutes until mushrooms darken and carrot bits are fork tender. Add tarragon and parsley and stir. Add wine and reduce liquid for 1 or 2 minutes. Add tomatoes to the sauce and stir to combine. Add chicken back to the pan and simmer chicken in sauce for 6 minutes or until chicken is cooked through and juices run clear.
Serve chicken with Herb and Butter Noodles and Sugar Snap Peas.
Toss the cooked egg noodles with butter bits and herbs in a bowl until butter melts, about 1 minute. Season noodles with salt and pepper.
Place snap peas in 1/2-inch boiling water with butter and a sprinkle of 1 teaspoon sugar. Reduce heat to simmer. Cover and steam snap peas 3 minutes. Remove cover and season snap peas with a little salt. Serve cooked snap peas with slotted spoon to allow for draining.