Grate the zest of one lemon. Squeeze the juice of three lemons and place it in a small pot with lemon zest and honey. Set the saucepan over low heat and simmer for 10 minutes.
Heat a frying pan with two tablespoons of olive oil. Season the chicken with salt and pepper. Transfer the chicken fillets to the pan and fry over high heat until the chicken is browned on both sides but still raw in the middle (about 2 minutes per side). Reduce the heat, add half the lemon-honey marinade and ½ cup of water, stir and cover tightly. Simmer the chicken covered 15 to 20 minutes.
Put the small potatoes in a pot and pour hot water over them until they are covered. Season with salt. Set over medium heat and cook for two minutes. Drain and pat dry. Transfer the potatoes to a heated frying pan and fry until browned on all sides, using the remaining olive oil. Season with dried herbs and stir. Remove from the heat. Using a slotted spoon, transfer to serving plates. Meanwhile, cut the broccoli into small florets and place in a pot of hot salted water. Cook for 3 minutes, drain.
Transfer the drained broccoli to serving plates. Add the cooked chicken and sprinkle chives and chili pepper over the food. Pour the remaining lemon-honey dressing over the meal and serve hot.