Wash the herbs, dab dry, put some tarragon aside for garnishing. Finely chop the rest. Wash lemons, rub dry. Peel fine strips from a lemon with a zest ripper, put aside.
Halve the lemon and squeeze it. Cook rice in boiling salted water for about 20 minutes. In the meantime season chicken fillets with salt and pepper and turn them in flour. Heat 1 tablespoon of oil in a pan and fry the fillets on each side for about 5 minutes until golden brown.
Wash the tomatoes, dab dry, scratch the skin slightly in one place. Place the tomatoes on a baking tray lined with baking paper, sprinkle with salt and sprinkle with 1 tablespoon of oil. Cook in a preheated oven (electric cooker: 200 °C/ convection oven: 175 °C/ gas: level 3) for approx. 8 minutes.
Add butter to the chicken and melt in the hot pan. Add lemon juice and herbs and bring to the boil once. Season with salt and pepper. Drain the rice. Cut the second lemon into slices, halve the slices.
Cut the chicken fillets open, arrange with lemon slices. Serve with rice, braised tomatoes and sauce. Garnish with tarragon and lemon peel.