It almost sounds like stewed chicken. Here's what I would do: Heat 2 tbsp. oil, brown chicken well on both sides, remove chicken to a plate. Saute garlic, onions and carrots for a few minutes (at this point, you can add herbs like 1 tsp. dried thyme or 1/2 tsp. each dried thyme and sage), add 2 tbsp. flour, stir for a couple of minutes to cook out the raw flour taste, then add 1 cup liquid (water or chicken stock), cook and stir over medium-high heat till it comes to a boil and thickens a little. Add chicken, reduce heat to low, cover and simmer till done, about 20 minutes.
The basic gravy recipe is to use 2 tbsp. oil and 2 tbsp. flour with 1 cup of water or stock; this can be doubled. The liquid must come to a boil or the gravy won't thicken.
The trouble with eating Italian food is that five or six days later you're hungry again. ~ George Miller