Wash the chicken breast fillets and pat dry. Season with salt and pepper. Coat lightly with some flour. Heat oil in a pan over medium-high heat. Fry the chicken for about 5-6 minutes per side until golden and the internal temperature reaches 74°C / 165°F. Remove to a plate.
Peel the onion and cut into fine cubes. Add to the same pan over medium heat and cook for about 3 minutes until softened. Stir in the crème fraîche and cream, and simmer for 2 minutes. Add the ajvar and mix well. Return the chicken to the pan and simmer for about 10 minutes until heated through.
Slice the chicken and arrange on plates with the sauce.