Heat a tablespoon of oil in a large frying pan, add a pile of spinach leaves and toss until they wilt. Transfer to a bowl and proceed with the remainder.
Lay the chicken breasts skin-side down on a cutting board, flatten them with your hands, and cut out the white tendon from the underside if visible.
Bring the stock to a boil in a medium to large saucepan and season with salt. Turn the heat down as low as possible. Immerse the chicken breasts in the stock and cook for 15 minutes without boiling. Transfer them to a plate and pat dry with paper towels. The stock can be used again: first pour it through a fine strainer, discarding any sediment in the bottom.
Heat 1/2 tablespoon of oil in a large frying pan over medium heat, season the chicken breasts well and cook for several minutes on each side until golden. You may need to do this in batches, or use two pans.
Just before the chicken is ready, heat a tablespoon of oil in another frying pan over medium heat. Add garlic and chile, and cook briefly until fragrant and lightly colored, then stir in the spinach, season with salt and heat through. Serve the chicken and spinach accompanied by lemon wedges.