Heat the oil in a saute pan, over medium-high heat.
Sprinkle salt and pepper over the chicken pieces, and place in a single layer in the pan.
Saute chicken until golden brown on each side.
Remove chicken from the pan and set aside.
Layer the onions, carrots, and celery in the bottom of a crock pot. Add the chicken pieces, and then the mushrooms.
Pour the chicken stock and white wine over.
Sprinkle the tarragon over everything.
Pop the garlic cubes out and let them sit on top of the chicken.
Cover, and cook on low for about 3 hours, or until chicken is fork tender, stirring once or twice to combine all of the ingredients.
To finish the sauce, remove the chicken and vegetables from the pot, and transfer the sauce to a large saucepan. Bring the sauce to a boil over high heat, and then reduce and simmer until the sauce is reduces by about half. You should have about 1 cup of sauce.
Return the reduced sauce to a crockpot, and stir in the Greek yogurt. Taste, and adjust seasoning with salt and pepper, and extra tarragon if desired.
Add the chicken and vegetables back to the crockpot and let warm through.
Serve with noodles, or garlic toast.