Chicken with broccoli and garlic sauce

Here is the recipe I promise.  It is really easy and uses stuff most of us have on hand which is great.
2 t olive oil
1 pound uncooked chicken breast cut in 1 inch pieces
1 t dried thym
1/2 t salt
1/4 t pepper
3 medium garlic cloves, minced
2 cups broccoli
1 1/2 cups chicken broth, divided
1 1/2 T cornstarch
2 cups cooked brown rice

-Heat oil in skillet, cook garlic stirring 1 minute
-season chicken with thyme, salt and pepper
-add chicken to oil and cook until browned on all sides
-add broccoli, cover and cook 2 minutes
-add 1 cup chicken broth, cover and simmer approximately 5 minutes
-in a cup, dissolve cornstarch in 1/2 cup broth, then add to skillet
-simmer until thickened, stirring occasionally
-serve over rice
For those of you who are gluten free, I don't know if cornstarch is gluten free but as long as you use gluten free broth, you are good to go.