Classic Grilled Chicken Caesar Salad Wraps

Name: Classic Grilled Chicken Caesar Salad Wraps
Ingredients: 4 medium-sized free-range chicken breasts; 2 tablespoons olive oil; Salt and freshly ground black pepper; For the Dressing:; 1 small clove garlic (crushed); 3 small anchovy fillets; 1 egg yolk; 1/2 teaspoon Dijon mustard; 2 teaspoons lemon juice; 1/2 cup extra-virgin olive oil; Salt and freshly ground black pepper (to taste); For the Wrap:; 1 Romaine lettuce, finely shredded; 2 oz. Parmesan shavings; 8 soft wraps (store-bought or homemade)