Marinate chicken with onion, olive oil, garlic, paprika and pepper for at least two hours.
Grill breast. Cut into thin slices. (Broiling works well, too - but nothing beats the grilled flavor.)
Combine green beans, carrots, red onion and chicken and parsley/cilantro.
Heat oil to 375 degrees F - making sure the oil fills only about half the depth of the pan you use. (See NOTE in intro.)
Fry potatoes until golden brown. Drain on paper towels.
Toss all ingredients with mayonnaise. Add salt and pepper to taste.
Garnish with parsley/cilantro leaves if desired.
Makes 5 servings.
ALTERNATE SERVING IDEA: Toss chicken, beans, carrots, red onion and parsley with mayonnaise. Mound in center of plate. Surround with fried potatoes or place fried potatoes on top of chicken salad mixture and garnish with parsley/cilantro sprigs.