In a heavy-bottomed pot, heat oil over medium-high heat. Season chicken with salt and pepper and sear until golden brown and cooked through, about 5 minutes per side. Set aside.
Add onion and celery and cook until tender, about 4 minutes. Deglaze with vinegar, scraping up any brown bits with a wooden spoon. Add sweet potatoes, collard greens, stock, and 2 cups water. Bring to a boil; reduce heat and simmer until sweet potatoes are tender, about 10 minutes.
Shred chicken, add to pot, and cook until heated through. Stir in rice and season with salt and pepper.