In a large skillet, heat oil over medium-high heat; brown chicken. Transfer to slow cooker.
To skillet, cook onions, celery, red pepper, garlic, thyme, salt and pepper until just lightly brown, about 6 minutes. Add to slow cooker.
Add broth or wine to slow cooker. Add bay leaves, tomatoes, tomato paste and 1/2 cup water. Cover and cook on low for 4 to 6 hours.
Discard bay leaves. Add kale and rice. Cover and cook on high for an additional 35-45 minutes.