Chop tamarind paste coarsely and bring to a boil in a saucepan with 125 ml (approximately 1/2 cup) of water. Stir well and strain through a sieve. Peel and press the garlic. Mix tamarind paste with garlic and curry paste and season with salt and sugar.
Score the skin of the chicken breasts and season with cayenne pepper. Rub all around with the tamarind paste mixture and refrigerate, covered, for 12 hours.
Heat the oil in an oven-proof pan over medium heat and brown the chicken breasts on the skin side. Bake in preheated oven at 190°C (approximately 375°F) with the skin side up for about 12 minutes. Then remove the meat from the oven, cut the breast meat off the bone in thin slices and serve.