Peel garlic and ginger, dice finely. Score the red chilli lengthways, remove seeds, wash, and finely chop. Mix together with the thyme.
Wash and pat dry the chicken breast fillets. Rub with the seasoning mixture, cover, and refrigerate for 1 hour.
Clean and wash the leeks, cut into rings. Heat 2 tablespoons oil in a large roasting pan over medium-high heat. Fry the chicken fillets on all sides until golden, about 3-4 minutes per side. Season with salt and pepper, then remove from the pan.
In the same pan, sauté the leeks over medium heat until softened, about 5 minutes. Add 2 tablespoons tomato paste and cook for 1 minute, stirring. Deglaze with 250 ml water and add the 425 ml canned tomatoes with their juice. Break up the tomatoes with a spoon. Season with salt and pepper, bring to a boil.
Place the chicken fillets on top of the sauce and pour the 150 ml cola over them. Cover the pan with a lid or foil. Place in a preheated oven at 200°C (392°F) for electric or gas level 3, or 175°C (347°F) for convection. Braise for 45 minutes, basting every 15 minutes, until chicken reaches 74°C (165°F) internal temperature.
Check the seasoning, adjust if needed, and serve with rice.