In a large pan (large enough to hold all the chicken in one layer, along with some sauce), brown the chicken in the oil. If you have a non-stick pan, you can omit the oil.
While the chicken is browning (or before), mix the tomato paste with the liquid from the canned mushrooms. Add more water if necessary -- the goal is to be able to pour the sauce, though it should still be pretty thick. (If you want to use fresh mushrooms, then you can just use water for this step.).
Sprinkle the chicken with the thyme, salt, and pepper.
Cover the chicken with the chopped onions.
Pour the tomato/liquid mixture on top of everything. Mix things together as well as you can. At this point it might seem like you won't have enough tomato sauce, but as the chicken and onions cook, they'll release their liquids and you'll have more sauce.
Cover and simmer for 40-45 minutes. Uncover occasionally to shift things around, flip the chicken over, and pour the sauce over the chicken. Add water as needed (but it might not be needed at all).
If you're using fresh mushrooms instead of canned, sauté them in a separate skillet.
When chicken is cooked, reduce the heat so that the sauce is no longer simmering. Add the yogurt, mushrooms, and parsley. Stir until everything is blended and warm.
Serve over rice (we use brown rice) -- you'll definitely want something to soak up all the yummy sauce!