Place the butter in a medium skillet and set over medium heat. Add the chopped onion and garlic. Saute for 3-5 minutes to soften, then pour the onions and butter into the crock of a large slow cooker.
Add the bouquet de garni and the chicken to the slow cooker. Sprinkle the chicken with 1 teaspoon salt, 1/2 teaspoon ground pepper, and 1/2 teaspoon paprika. Pour the rice over the top and lay the lemon slices over it. Then pour the chicken broth over the rice.
Cover and cook on high for 2-3 hours, or on low for 3-5 hours. (The first time you make this dish, be watchful of the rice. All slow cookers are slightly different, and you do not want the rice to cook to mush. Turn the slow cooker off when the rice is firm and fluffy. My slow cooker takes 2 hours on high.)
Pull the chicken breast and the bouquet de garni out of the crock and cut into bite-size chunks. Add the chicken back to the crock and toss. Serve warm.
NOTES: You can substitute 1 tablespoon dried Herbs de Provence for the bouquet de garni.