In a large skillet, brown chicken in 2 tablespoons oil.
Remove chicken from heat and place in a large serving casserole.
Add the broccoli. Sauté mushrooms in remaining oil in the skillet Add tarragon and sauté for 5 minutes Add the wine and broth and simmer for 5 minutes.
Pour sauce over the chicken and broccoli and bake uncovered for 30 minutes.