In a small Dutch oven or a large soup pot, heat the oil over medium-high heat. Sprinkle the chicken thighs on both sides with salt and pepper; put them in the pan, fattier side down, and cook until browned on the bottom and some of the fat has rendered out, 4 minutes. Flip the thighs over, tuck the garlic in around them and cook until the garlic is browned and aromatic, about 1 minute. Pour in the chicken stock and simmer until the thighs are cooked through, about 12 minutes. Remove the thighs from the pot and cut into bite-size pieces.
While the soup is cooking, cut the leaves of the escarole away from the core and wash well in cold water, especially the white part near the base, where most of the dirt collects. Tear the leaves into 2-inch pieces.
Stir the escarole into the pot a handful at a time until it all fits, then cover and cook until tender, 3 minutes. Return the chicken to the pot and bring back to a simmer. Serve hot.
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