How to Make It
Season chicken on all sides with salt and pepper. Melt butter with oil in a large skillet over medium-high heat. Working in batches, add chicken and cook, turning often, until browned on all sides, 5 to 7 minutes. Transfer to a large slow cooker.
Pour off all but 1 Tbsp. fat from skillet. Add onion and cook, stirring often, until softened, about 3 minutes. Add garlic and sauté for 30 seconds. Add tomatoes and bring to a boil, stirring to pick up any browned bits on bottom of skillet. Stir in beans and thyme.
Pour contents of skillet over chicken in slow cooker. Cover and cook on low until chicken is tender and beans are soft, 3 to 4 hours. Transfer chicken to a platter and cover loosely with foil. Set cooker on high and bring bean mixture to a simmer. Cook, uncovered, until reduced and thickened, about 10 minutes. Season with salt and pepper. Discard thyme sprigs. Spoon beans over chicken on platter, then serve immediately.