Place wooden skewers in water. Rinse chicken breast fillets, pat dry and cut into 2 cm (approximately 3/4-inch) cubes. Halve and squeeze limes. Thread chicken cubes onto the soaked skewers.
Combine paprika, cayenne pepper, 3 tablespoons lime juice, tamarind paste and ketchup. Place skewers in a container and cover with plastic wrap. Place in refrigerator to marinate for at least 2 hours.
Meanwhile, rinse the tomatoes and cut into quarters, removing stems. Seed tomatoes and cut each quarter in half crosswise. Peel the onion and chop coarsely. Halve chile pepper, remove the seeds, rinse thoroughly and chop finely. Halve avocados and remove the pits. Gently work a spoon between flesh and skin of avocado, removing the fruit. Cut into large cubes.
Rinse cilantro, pat dry and chop the leaves. Combine 1 tablespoon lime juice, tomatoes, onion, chile pepper and avocado, and season with salt and pepper.
Arrange skewers in a grill pan or on a charcoal grill and cook over medium heat for 7-8 minutes. Serve with avocado and tomato salad.