Rinse the chicken breast fillets and pat dry. Season with salt and pepper.
Heat the olive oil in a pan over medium heat. Sear the chicken on the skin side for 2-3 minutes, then turn and fry over low heat for 10 minutes until the internal temperature reaches 74°C / 165°F. Transfer to a warm plate.
In the same pan, add the sugar and let it caramelize over medium heat for 2-3 minutes. Deglaze with the balsamic vinegar and poultry broth. Stir in the crème fraîche. Simmer the sauce for 5 minutes.
Wash, core, and dice the tomatoes. Rinse the basil, shake dry, pluck the leaves, and chop finely. Add the tomatoes and basil to the sauce, heat through for 1-2 minutes, and season with salt and pepper.
Slice the chicken breast fillets and arrange on serving plates. Pour the sauce over them and garnish with basil if desired.