Preheat oven to 350 degrees F.
Place chicken breasts in a 9x13 pan.
Drain the pineapple chunks (set chunks aside), pouring the juice over the chicken breasts. Cover with aluminum foil and bake in the oven for 1 hour.
In a medium saucepan, combine barbecue sauce, orange juice, brown sugar, vegetable oil, flour, salt, and ginger. Cook over medium heat until it comes to a boil and slightly thickens. Remove from heat and set aside.
After the chicken has cooked for 1 hour, remove it from the oven and cover it with the sauce from the saucepan. Reserve about ¼ cup of sauce for later. Return chicken to the oven, uncovered, for 30 minutes.
Remove the pan and top the chicken with drained pineapple chunks and drained mandarin slices. Return chicken to the oven and bake for 5 minutes. Now you want to reheat the ¼ cup leftover sauce, either in its pan or in a microwave-safe bowl.
Remove chicken from the oven. With the remaining sauce, coat the chicken one more time. If you still have some sauce left, add a little pineapple juice and thin slightly. This will create a yummy, thinner sauce that can be poured over the rice.
Individually plate each piece of chicken over rice. Or you can place all the pieces on a platter and serve the rice on the side.