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Preheat oven to 350 degrees. Place the apricots in a saucepan and cover with water. Heat until boiling and then reduce to a simmer. Continue to cook until the apricots soften, about 15 minutes. Remove the apricots and set aside, reserving the water.
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In a very large baking dish pour some of the reserved water on the bottom of the pan. Add the chicken. Sprinkle the chicken with, salt, pepper, paprika and garlic. Rub this onto the chicken. Drizzle the oil over the chicken.
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Place the carrots and the apricots around the chicken. Put the dish into the oven. Bake for 1 1/4 hours. In between, check to see that the carrots and the apricots don't dry out. Mix them into the pan drippings.
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After 1 1/4 hours, brush the Saucy Susan all over the chicken and bake for about 15 more minutes. Check to see if the chicken is done by inserting a knife into the breast. If juices run clear it is done. If not continue baking for another 10 minutes. Remove and let rest for 10 minutes before serving.