Lightly coat a 6-quart slow cooker with nonstick cooking spray or oil. Add chicken, onion, and garlic to the slow cooker. Add curry powder, ginger, salt, and pepper to the slow cooker. Toss to coat. Stir in drained beans, undrained tomatoes, broth, and bay leaf. Cover and cook on high-heat setting 4 to 5 hours or low-heat setting 8 to 10 hours.
Stir lime juice into cooked stew. Stir spinach leaves into stew and let stand 2 to 3 minutes to wilt. Serve with rice.