Bring a large volume of salted water (10 g of coarse salt per litre) to a boil.
Wash the arugula, and immerse it in boiling water for 4 minutes. Drain the arugula, and mix in a food processor with some cooking water.
Add olive oil to emulsify the sauce, and adjust the seasoning. Set aside.
Cut the chicken breast into thin slices. Then cut the slices into sticks of about 0.5 cm thick. Salt.
Brown the chicken pieces in a hot frying pan with olive oil, then remove.
Pour more olive oil in the same pan, and add the roasted peppers and drained olives. Fry everything quickly, then add the arugula coulis, and mix the combination.
Place the chicken slices back in the pan, and cook for 4 to 5 minutes. Adjust seasoning to taste.
Transfer the preparation to a shallow dish, and serve with a garnish of fresh arugula.