Heat oil over high heat in a large saucepan or Dutch oven. Saute chicken in oil until both sides are browned, approximately 2 minutes per side. Remove the chicken, and set aside.
Add onions and garlic to saucepan, and saute until golden. Stir in the tomatillos, jalapeno peppers, and broth. Bring to a boil. Reduce heat, cover the pot, and simmer for about 15 minutes.
Puree vegetables in batches in a blender or food processor. Return to pot, and reheat. At this point taste the soup; if not piquant enough, add cayenne pepper or pepper sauce.
Slice the chicken into thin slices, and then shred. Stir into soup. Season to taste with salt and pepper.
When ready to serve, stir in the minced cilantro and ladle into bowls. Put a dollop of sour cream on top of each portion, and let it melt a bit. Top each dollop with a single cilantro leaf, and serve immediately.